009B Sample Final 1, Problem 5

Consider the solid obtained by rotating the area bounded by the following three functions about the $y$-axis:

$x=0$, $y=e^{x}$, and $y=ex$.

a) Sketch the region bounded by the given three functions. Find the intersection point of the two functions:

$y=e^{x}$ and $y=ex$. (There is only one.)

b) Set up the integral for the volume of the solid.

c) Find the volume of the solid by computing the integral.