Chapter 8, Problem 46RE

To determine

To find : the volume of the solid.

Answer to Problem 46RE

The volume of the solid is $2{\pi }^2$ .

Explanation of Solution

Given information : The region bounded by the curves about the y-axis $y=\sin x,y=0,0\le x\le \pi$ .

Calculation :

From the cylindrical shell method:

  $V={\displaystyle \underset{a}{\overset{b}{\int }}2\pi xf\left(x\right)dx}$

With $f\left(x\right)$ the function that bounds the region is bounded.

  $\begin{array}{l}V={\displaystyle \underset{0}{\overset{\pi }{\int }}2\pi x\left(\sin x\right)}dx\\ V=2{\pi }^2\end{array}$