Describe the solid whose volume is represented by the following definite integrals.

The integral of 2pi(x-1)e^x from 2 to 7.

1 answer

Looks like the curve y=e^x on the interval [2,7] rotated around the line x=1.

I assume you meant to include dx in the integral.

Since the volume of a shell of thickness dx is 2πrh dx,

if r = x-1 and h=e^x

that fits the bill.