The region between the graphs of y=x^2 and y=2x is rotated around the line x=2.

Question

how do you find the volume of the object?

Answer 1

First find the enclosed region between the curves. It looks like it goes from (x = 0, y = 0) to (x = 2, y = 4)

Then perform the integration from x = 0 to 2 of 2 pi(2x - x^2)(2-x)dx. This is a series of thin ring-shaped areas centered on the x=2 vertical line

Answer 2

64pi/6