<?xml version='1.0' encoding='UTF-8'?>
<exercise xmlns="https://spatext.clontz.org" version="0.0">
<statement>
<ol>
<li>
Compute the Laplace transform of
<m>y = {{pretransform}}</m> by using a transform table.
</li>
<li>
Show why <m>\mathcal{L}\{ {{e_pretransform}} \}={{e_transform}}</m>
using the integral definition of a Laplace transform.
</li>
</ol>
</statement>
<answer>
<ol>
<li>
<me>
\mathcal{L}\{y\} = {{transform}}
</me>
</li>
<li>
<me>
\mathcal{L}\{ {{e_pretransform}} \}
=\int_0^{\infty} {{e_pretransform}} e^{-st}\,dt
={{e_transform}}
</me>
</li>
</ol>
</answer>
</exercise>