Chapter 6.4, Problem 75E

(a)

To determine

To show: The volume of the solid when the region is revolved about the vertical line $x=x_0$ using shell method is $V={\displaystyle \underset{a}{\overset{b}{\int }}\pi \left({\left(f\left(x\right)-y_0\right)}^2-{\left(g\left(x\right)-y_0\right)}^2\right)dx}$.

(b)

To determine

To show: The volume of the solid when the region is revolved about the vertical line $x=x_0$ using shell method is $V={\displaystyle \underset{a}{\overset{b}{\int }}\pi \left({\left(f\left(x\right)-y_0\right)}^2-{\left(g\left(x\right)-y_0\right)}^2\right)dx}$.