Chapter 6.2, Problem 2QCE

A solid $S$ is generated by revolving the region between the $x\text{-axis}$ and the curve $y=\sqrt{\sin x}\left(0\le x\le \pi \right)$ about the $x\text{-axis}$ .

(a) For $x$ between $0$ and $\pi$ , the cross-sectional areal of $S$ perpendicular to the $x\text{-axis}$ at $x$ is $A\left(x\right)=\text{\_\_\_\_\_\_\_\_}$ .

(b) An integral expression for the volume of $S$ is $\text{\_\_\_\_\_\_\_\_}$ .

(b) The value of the integral in part (b) is $\text{\_\_\_\_\_\_\_\_}$ .