Problem with this question on solid of revolution

Question

Calculate the volume of a revolution solid obtained by rotation around the x-axis, the region bounded by the graph of $y=e^x$, $-1\le x \le1$ and the x-axis.

Thanks in advance, and sorry about my english.

Answer 1

\begin{align*} V&=\pi\int_a^b f^2(x)\,dx\\ &=\pi\int_{-1}^1 \left( e^x \right) ^2\,dx\\ &=\pi\int_{-1}^1 e^{2x}\,dx\\ &=\pi\left[\frac12 e^{2x} \right]_{-1}^1\\ &=\pi\left( \frac{e^2}{2} - \frac{e^{-2}}{2} \right)\\ &=\frac{\pi}{2}\left( e^2 - e^{-2} \right) \end{align*}