The region $R$ is bounded by the part of the curve $y = (x - 2)^{\frac{3}{2}}$ for which \(2 \le

Question

The region $R$ is bounded by the part of the curve $y = (x - 2)^{\frac{3}{2}}$ for which $2 \leq x \leq 4$, the $x$-axis, and the lines $x = 2$ and $x = 4$. Find, in terms of $\pi$, the volume of the solid obtained when $R$ is rotated through four right angles about the $x$-axis.

Accepted Answer

$4 \pi$ unit$^3$.

Volume of solid of revolution about x-axis

Volume of solid of revolution about x-axis