Chapter 8.1, Problem 72E

a.

To determine

Find the volume of the solid of revolution that results when the region under the graph of $f\left(x\right)=e^{-x}\text{ for }0\le x\le 1$ is revolved around the y-axis.

b.

To determine

Find the volume of the solid of revolution that results when the region under the graph of $f\left(x\right)=e^{-x}\text{ for }0\le x\le 1$ is revolved around the line $x=1$