D1.qti

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<questestinterop xmlns="http://www.imsglobal.org/xsd/ims_qtiasiv1p2" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.imsglobal.org/xsd/ims_qtiasiv1p2 http://www.imsglobal.org/xsd/ims_qtiasiv1p2p1.xsd">
  <objectbank ident="D1">
    <qtimetadata>
      <qtimetadatafield><fieldlabel>bank_title</fieldlabel><fieldentry>Differential Equations -- D1</fieldentry></qtimetadatafield>
    </qtimetadata>
  <item ident="D1-3590" title="D1 | Discontinuous functions and distributions | ver. 3590"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" alt="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 2 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0932" title="D1 | Discontinuous functions and distributions | ver. 0932"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" alt="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" title="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" data-latex="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%209" alt="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" title="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" data-latex="\int_{ 2 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5967" title="D1 | Discontinuous functions and distributions | ver. 5967"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1330" title="D1 | Discontinuous functions and distributions | ver. 1330"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" alt="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%206" alt="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 2 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5042" title="D1 | Discontinuous functions and distributions | ver. 5042"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2287" title="D1 | Discontinuous functions and distributions | ver. 2287"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%206" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9723" title="D1 | Discontinuous functions and distributions | ver. 9723"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%209" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-6205" title="D1 | Discontinuous functions and distributions | ver. 6205"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" alt="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" title="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" data-latex="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%206" alt="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" title="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" data-latex="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8484" title="D1 | Discontinuous functions and distributions | ver. 8484"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" alt="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2567" title="D1 | Discontinuous functions and distributions | ver. 2567"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" alt="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" title="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" data-latex="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%208" alt="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" title="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" data-latex="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1633" title="D1 | Discontinuous functions and distributions | ver. 1633"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" alt="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2020" alt="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-3914" title="D1 | Discontinuous functions and distributions | ver. 3914"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2010" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-3719" title="D1 | Discontinuous functions and distributions | ver. 3719"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" alt="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" title="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" data-latex="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" title="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" data-latex="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9156" title="D1 | Discontinuous functions and distributions | ver. 9156"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" alt="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%208" alt="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 1 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2364" title="D1 | Discontinuous functions and distributions | ver. 2364"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" alt="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" title="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" data-latex="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%204" alt="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" title="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" data-latex="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1275" title="D1 | Discontinuous functions and distributions | ver. 1275"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" alt="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 4 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7553" title="D1 | Discontinuous functions and distributions | ver. 7553"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" alt="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%206" alt="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9942" title="D1 | Discontinuous functions and distributions | ver. 9942"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%209" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-3254" title="D1 | Discontinuous functions and distributions | ver. 3254"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2010" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9241" title="D1 | Discontinuous functions and distributions | ver. 9241"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%206" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5478" title="D1 | Discontinuous functions and distributions | ver. 5478"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2829" title="D1 | Discontinuous functions and distributions | ver. 2829"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" alt="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8497" title="D1 | Discontinuous functions and distributions | ver. 8497"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" alt="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%208" alt="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7137" title="D1 | Discontinuous functions and distributions | ver. 7137"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" alt="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" title="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" data-latex="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" title="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12" data-latex="\int_{ 2 }^{ 9 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 9 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9740" title="D1 | Discontinuous functions and distributions | ver. 9740"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2020" alt="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" title="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" data-latex="\int_{ 2 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-4465" title="D1 | Discontinuous functions and distributions | ver. 4465"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" alt="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" title="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" data-latex="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%209" alt="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" title="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" data-latex="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7981" title="D1 | Discontinuous functions and distributions | ver. 7981"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" alt="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" title="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" data-latex="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2020" alt="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" title="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20" data-latex="\int_{ 1 }^{ 7 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 7 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 20"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7408" title="D1 | Discontinuous functions and distributions | ver. 7408"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" alt="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" title="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" data-latex="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%208" alt="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" title="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" data-latex="\int_{ 2 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0148" title="D1 | Discontinuous functions and distributions | ver. 0148"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2020" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7560" title="D1 | Discontinuous functions and distributions | ver. 7560"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" alt="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 0 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-3085" title="D1 | Discontinuous functions and distributions | ver. 3085"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" alt="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 1 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5116" title="D1 | Discontinuous functions and distributions | ver. 5116"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" alt="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" title="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" data-latex="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%209" alt="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" title="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" data-latex="\int_{ 0 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-4824" title="D1 | Discontinuous functions and distributions | ver. 4824"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 16" alt="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 16" title="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 16" data-latex="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 16"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2016" alt="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 16" title="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 16" data-latex="\int_{ 3 }^{ 10 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 10 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 16"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5956" title="D1 | Discontinuous functions and distributions | ver. 5956"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-6485" title="D1 | Discontinuous functions and distributions | ver. 6485"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%209" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0834" title="D1 | Discontinuous functions and distributions | ver. 0834"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" alt="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" title="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" data-latex="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%209" alt="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" title="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" data-latex="\int_{ 3 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7683" title="D1 | Discontinuous functions and distributions | ver. 7683"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1665" title="D1 | Discontinuous functions and distributions | ver. 1665"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%209" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7049" title="D1 | Discontinuous functions and distributions | ver. 7049"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2577" title="D1 | Discontinuous functions and distributions | ver. 2577"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 4" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 4" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 4" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%204" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 4" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 4" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0354" title="D1 | Discontinuous functions and distributions | ver. 0354"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" alt="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" title="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" data-latex="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%209" alt="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" title="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" data-latex="\int_{ 1 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 1 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5438" title="D1 | Discontinuous functions and distributions | ver. 5438"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8883" title="D1 | Discontinuous functions and distributions | ver. 8883"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%208" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1043" title="D1 | Discontinuous functions and distributions | ver. 1043"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" alt="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" title="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" data-latex="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%208" alt="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" title="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" data-latex="\int_{ 3 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7931" title="D1 | Discontinuous functions and distributions | ver. 7931"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%208" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2514" title="D1 | Discontinuous functions and distributions | ver. 2514"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 6" alt="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 6" title="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 6" data-latex="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%206" alt="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 6" title="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 6" data-latex="\int_{ 0 }^{ 5 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 5 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5728" title="D1 | Discontinuous functions and distributions | ver. 5728"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" alt="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" title="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" data-latex="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" title="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" data-latex="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7421" title="D1 | Discontinuous functions and distributions | ver. 7421"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" alt="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" title="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" data-latex="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%208" alt="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" title="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8" data-latex="\int_{ 4 }^{ 8 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 4 }^{ 8 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-3390" title="D1 | Discontinuous functions and distributions | ver. 3390"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" alt="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" title="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" data-latex="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%209" alt="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" title="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9" data-latex="\int_{ 4 }^{ 8 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 8 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2367" title="D1 | Discontinuous functions and distributions | ver. 2367"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" alt="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%208" alt="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 3 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5018" title="D1 | Discontinuous functions and distributions | ver. 5018"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%209" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5863" title="D1 | Discontinuous functions and distributions | ver. 5863"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2020" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-3146" title="D1 | Discontinuous functions and distributions | ver. 3146"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9464" title="D1 | Discontinuous functions and distributions | ver. 9464"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" alt="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204" alt="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-6513" title="D1 | Discontinuous functions and distributions | ver. 6513"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" alt="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" title="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" data-latex="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%204" alt="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" title="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4" data-latex="\int_{ 3 }^{ 7 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 7 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-3529" title="D1 | Discontinuous functions and distributions | ver. 3529"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" alt="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" title="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" data-latex="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2016" alt="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" title="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" data-latex="\int_{ 1 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8834" title="D1 | Discontinuous functions and distributions | ver. 8834"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" alt="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" title="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" data-latex="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%208%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2016" alt="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" title="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16" data-latex="\int_{ 2 }^{ 8 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 2 }^{ 8 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 16"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2371" title="D1 | Discontinuous functions and distributions | ver. 2371"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" alt="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" title="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" data-latex="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2010" alt="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" title="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" data-latex="\int_{ 1 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 1 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5691" title="D1 | Discontinuous functions and distributions | ver. 5691"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9687" title="D1 | Discontinuous functions and distributions | ver. 9687"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%206" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9801" title="D1 | Discontinuous functions and distributions | ver. 9801"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" alt="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204" alt="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 1 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5290" title="D1 | Discontinuous functions and distributions | ver. 5290"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" alt="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" title="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" data-latex="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%208" alt="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" title="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" data-latex="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-3130" title="D1 | Discontinuous functions and distributions | ver. 3130"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%206" alt="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 2 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9605" title="D1 | Discontinuous functions and distributions | ver. 9605"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 4" alt="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 4" title="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 4" data-latex="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204" alt="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 4" title="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 4" data-latex="\int_{ 3 }^{ 6 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 6 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5742" title="D1 | Discontinuous functions and distributions | ver. 5742"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%208%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%208" alt="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 3 }^{ 8 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 8 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8424" title="D1 | Discontinuous functions and distributions | ver. 8424"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2020" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-4468" title="D1 | Discontinuous functions and distributions | ver. 4468"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%209" alt="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" title="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" data-latex="\int_{ 2 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 2 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-6473" title="D1 | Discontinuous functions and distributions | ver. 6473"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0942" title="D1 | Discontinuous functions and distributions | ver. 0942"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" alt="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" title="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" data-latex="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%209" alt="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" title="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9" data-latex="\int_{ 3 }^{ 7 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 7 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0488" title="D1 | Discontinuous functions and distributions | ver. 0488"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" alt="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" title="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" data-latex="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%208" alt="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" title="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8" data-latex="\int_{ 0 }^{ 7 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 7 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8397" title="D1 | Discontinuous functions and distributions | ver. 8397"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" alt="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" title="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" data-latex="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2010" alt="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" title="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10" data-latex="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9500" title="D1 | Discontinuous functions and distributions | ver. 9500"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 15" alt="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 15" title="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 15" data-latex="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 15" title="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 15" data-latex="\int_{ 3 }^{ 7 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 3 }^{ 7 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9301" title="D1 | Discontinuous functions and distributions | ver. 9301"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 16" alt="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 16" title="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 16" data-latex="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 16"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2016" alt="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 16" title="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 16" data-latex="\int_{ 0 }^{ 7 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 0 }^{ 7 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 16"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5370" title="D1 | Discontinuous functions and distributions | ver. 5370"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" alt="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" title="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" data-latex="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%206" alt="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" title="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" data-latex="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5812" title="D1 | Discontinuous functions and distributions | ver. 5812"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" alt="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 5 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 5 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1153" title="D1 | Discontinuous functions and distributions | ver. 1153"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%208" alt="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" title="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8" data-latex="\int_{ 3 }^{ 9 } 2 \, \delta\left(t - 5\right) \,dt = 2 \hspace{2em} \int_{ 3 }^{ 9 } 2 \, \mathrm{u}\left(t - 5\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8795" title="D1 | Discontinuous functions and distributions | ver. 8795"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" alt="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0627" title="D1 | Discontinuous functions and distributions | ver. 0627"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%209" alt="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" title="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9" data-latex="\int_{ 4 }^{ 9 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 9 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1179" title="D1 | Discontinuous functions and distributions | ver. 1179"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" alt="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%2010%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 3 }^{ 10 } 3 \, \delta\left(t - 6\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 10 } 3 \, \mathrm{u}\left(t - 6\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9158" title="D1 | Discontinuous functions and distributions | ver. 9158"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" alt="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204" alt="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 0 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 0 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5625" title="D1 | Discontinuous functions and distributions | ver. 5625"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" alt="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%206" alt="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 1 }^{ 7 } 2 \, \delta\left(t - 4\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 7 } 2 \, \mathrm{u}\left(t - 4\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-6939" title="D1 | Discontinuous functions and distributions | ver. 6939"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7875" title="D1 | Discontinuous functions and distributions | ver. 7875"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" alt="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%206%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%206" alt="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" title="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6" data-latex="\int_{ 3 }^{ 6 } 3 \, \delta\left(t - 4\right) \,dt = 3 \hspace{2em} \int_{ 3 }^{ 6 } 3 \, \mathrm{u}\left(t - 4\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8935" title="D1 | Discontinuous functions and distributions | ver. 8935"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt = 8" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt = 8" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt = 8" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%208" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt = 8" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt = 8" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 5\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 5\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-9295" title="D1 | Discontinuous functions and distributions | ver. 9295"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 0 }^{ 7 } 3 \, \delta\left(t - 3\right) \,dt = 3 \hspace{2em} \int_{ 0 }^{ 7 } 3 \, \mathrm{u}\left(t - 3\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-2440" title="D1 | Discontinuous functions and distributions | ver. 2440"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" alt="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" title="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" data-latex="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%208%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" title="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15" data-latex="\int_{ 4 }^{ 8 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 8 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5144" title="D1 | Discontinuous functions and distributions | ver. 5144"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" alt="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%209%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" title="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12" data-latex="\int_{ 3 }^{ 9 } 4 \, \delta\left(t - 6\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 9 } 4 \, \mathrm{u}\left(t - 6\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7683" title="D1 | Discontinuous functions and distributions | ver. 7683"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%205%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204" alt="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" title="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4" data-latex="\int_{ 2 }^{ 5 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 5 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8659" title="D1 | Discontinuous functions and distributions | ver. 8659"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" alt="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" title="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" data-latex="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%206" alt="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" title="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" data-latex="\int_{ 1 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 1 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8522" title="D1 | Discontinuous functions and distributions | ver. 8522"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" alt="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" title="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" data-latex="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%205%20%7D%5E%7B%2010%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%208" alt="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" title="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8" data-latex="\int_{ 5 }^{ 10 } 2 \, \delta\left(t - 6\right) \,dt = 2 \hspace{2em} \int_{ 5 }^{ 10 } 2 \, \mathrm{u}\left(t - 6\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0314" title="D1 | Discontinuous functions and distributions | ver. 0314"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" alt="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" title="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" data-latex="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%200%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" title="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15" data-latex="\int_{ 0 }^{ 6 } 5 \, \delta\left(t - 3\right) \,dt = 5 \hspace{2em} \int_{ 0 }^{ 6 } 5 \, \mathrm{u}\left(t - 3\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8156" title="D1 | Discontinuous functions and distributions | ver. 8156"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" alt="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%2020" alt="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" title="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20" data-latex="\int_{ 2 }^{ 9 } 5 \, \delta\left(t - 5\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 9 } 5 \, \mathrm{u}\left(t - 5\right) \,dt = 20"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8230" title="D1 | Discontinuous functions and distributions | ver. 8230"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%203%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 3 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 3 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1219" title="D1 | Discontinuous functions and distributions | ver. 1219"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" alt="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%207%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" title="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12" data-latex="\int_{ 1 }^{ 7 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 7 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-4781" title="D1 | Discontinuous functions and distributions | ver. 4781"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%209%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%206%5Cright)%20%5C,dt%20=%2015" alt="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" title="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15" data-latex="\int_{ 4 }^{ 9 } 5 \, \delta\left(t - 6\right) \,dt = 5 \hspace{2em} \int_{ 4 }^{ 9 } 5 \, \mathrm{u}\left(t - 6\right) \,dt = 15"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-5483" title="D1 | Discontinuous functions and distributions | ver. 5483"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" alt="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" title="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" data-latex="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%202%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%202%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%206" alt="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" title="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6" data-latex="\int_{ 2 }^{ 6 } 2 \, \delta\left(t - 3\right) \,dt = 2 \hspace{2em} \int_{ 2 }^{ 6 } 2 \, \mathrm{u}\left(t - 3\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-1753" title="D1 | Discontinuous functions and distributions | ver. 1753"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%205%20%5Chspace%7B2em%7D%20%5Cint_%7B%202%20%7D%5E%7B%206%20%7D%205%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%2010" alt="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" title="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10" data-latex="\int_{ 2 }^{ 6 } 5 \, \delta\left(t - 4\right) \,dt = 5 \hspace{2em} \int_{ 2 }^{ 6 } 5 \, \mathrm{u}\left(t - 4\right) \,dt = 10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-7362" title="D1 | Discontinuous functions and distributions | ver. 7362"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%204%5Cright)%20%5C,dt%20=%208" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 4\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 4\right) \,dt = 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-8145" title="D1 | Discontinuous functions and distributions | ver. 8145"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" alt="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt" alt="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" title="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt" data-latex="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" alt="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" title="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" data-latex="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%204%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cdelta%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%203%20%5Chspace%7B2em%7D%20%5Cint_%7B%204%20%7D%5E%7B%207%20%7D%203%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%205%5Cright)%20%5C,dt%20=%206" alt="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" title="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6" data-latex="\int_{ 4 }^{ 7 } 3 \, \delta\left(t - 5\right) \,dt = 3 \hspace{2em} \int_{ 4 }^{ 7 } 3 \, \mathrm{u}\left(t - 5\right) \,dt = 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="D1-0911" title="D1 | Discontinuous functions and distributions | ver. 0911"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>D1.</strong></p><p> Illustrustrate both of the following integrals. Then explain how to compute each. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Illustrustrate both of the following integrals. Then explain how to compute each. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cdelta%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%204%20%5Chspace%7B2em%7D%20%5Cint_%7B%201%20%7D%5E%7B%206%20%7D%204%20%5C,%20%5Cmathrm%7Bu%7D%5Cleft(t%20-%203%5Cright)%20%5C,dt%20=%2012" alt="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" title="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12" data-latex="\int_{ 1 }^{ 6 } 4 \, \delta\left(t - 3\right) \,dt = 4 \hspace{2em} \int_{ 1 }^{ 6 } 4 \, \mathrm{u}\left(t - 3\right) \,dt = 12"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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</questestinterop>