Find the volume of the generated solid

Question

The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(ex) is rotated about the x-axis. What is the volume of the generated solid?

A:  0.906

B. 0.795

C. 2.846

D. 2.498

I graphed it but that's about it. Not sure where to go from here.

Answer 1

Did you learn volumes of revolution yet?

To get a volume formed by revolving a graph around the x-axis, you add up (by integrating) a bunch of cylindrical disks. Each disk volume is πr²h, where r is the function, and h is "dx". Then you add (integrate) all the disks from the lower bound to the upper bound.

What do you get by doing that here? (this problem is a calculator problem, because no one is doing the integral of sin(e^x) with or without the square. Do you need help doing integrals on the graphing calculator?)