# Volume of the solid of revolution for $f(x)=\sin x$

## Answer

\[V=\int_0^{\pi}\pi \sin ^2 x dx=\pi \int_0^{\pi}\frac{1-\cos 2x}{2}dx\]

\[=\pi \left( \frac{x}{2}-\frac{\sin 2x}{4} \right) \bigg |_{x=0}^{x=\pi}=\pi (\frac{\pi}{2}-0)\]

\[=\frac{\pi^2}{2}.\]

The answer is accepted.

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