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

Find the colume of the solid obtained by rotating the graph of the function $y=\sin x$ around $x$-axis between $x=0$ and $x=\pi$.

$V=\int_0^{\pi}\pi \sin ^2 x dx=\pi \int_0^{\pi}\frac{1-\cos 2x}{2}dx$
$=\pi \left( \frac{x}{2}-\frac{\sin 2x}{4} \right) \bigg |_{x=0}^{x=\pi}=\pi (\frac{\pi}{2}-0)$
$=\frac{\pi^2}{2}.$