0004.qti

<item ident="D1-5042" title="D1 | Discontinuous functions and distributions | ver. 5042">
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  <presentation>
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        <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"/>
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      <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;

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          <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>
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        <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;

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