Answer
$\displaystyle{V=\frac{\pi }{2}\left(e^{2}-e^{-2}\right)}\\ $
Work Step by Step
$\displaystyle{A\left(x\right)=\pi \left(e^x\right)^2}\\ \displaystyle{A\left(x\right)=\pi \left(e^{2x}\right)}\\$
$\displaystyle{V=\int_{-1}^1A\left(x\right)\ dx}\\
\displaystyle{V=\int_{-1}^1\pi \left(e^{2x}\right)\ dx}\\
\displaystyle{V=\pi \int_{-1}^1e^{2x}\ dx}\\
\displaystyle{V=\pi\left[\frac{1}{2}e^{2x}\right]_{-1}^1}\\
\displaystyle{V=\pi\left(\left(\frac{1}{2}e^{2}\right)-\left(\frac{1}{2}e^{-2}\right)\right)}\\
\displaystyle{V=\frac{\pi }{2}\left(e^{2}-e^{-2}\right)}\\ $
