Chapter 8, Problem 47RE

To determine

To find : the volume of the solid.

Answer to Problem 47RE

The volume of the solid is $\frac{16\pi }{3}$ .

Explanation of Solution

Given information : The region bounded by the curves about the y-axis $y=x-3,y=x^2-3x$ .

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.

  $\begin{array}{l}V={\displaystyle \underset{1}{\overset{3}{\int }}2\pi x\left(x-3-x^2+3x\right)}dx\\ V=\frac{16\pi }{3}\end{array}$