Find the area of the region between for in .

Name: Find the area of the region between for in .
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Question

Find the area of the region between  for  in  .

Quizplus · Accepted Answer

The region between the curves is bounded by two vertical lines at $x = -2$ and $x=3$. Thus, we integrate with respect to $x$ as follows: \begin{align*}
\int_{-2}^3 [(x+2)^3 - (x-3)^3] dx &= \left[\frac{(x+2)^4}{4} - \frac{(x-3)^4}{4}ight]_{-2}^3\
&= \frac{(5)^4}{4} - \frac{(-5)^4}{4}\
&= \frac{625-625}{4}\
&= \boxed{0}
\end{align*}

Find the Area of the Region Between for