Volume of revolution about the x-axis (2)

Text

The region bounded by $y=\sqrt{x}$, the $x$-axis and $x=4$ is revolved about the $x$-axis. Compute the volume of the solid.

Solution

Disk method: $V=\pi\displaystyle\int_0^4 x\,dx=\pi\Big[\tfrac{x^{2}}{2}\Big]_0^4=8\pi\approx25.133$. $\boxed{V=8\pi\approx25.133}$