Help with calculus please

Question

Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y = e^x, x = 2, and y = 1 is revolved around the line y = -1.

Options:

1)
2)
3)
4)

Answer 1

Answer is 4, using the disk method. So, you take the area of the outer disk and then subtract the inner disk area. Outer disk has radius of ( y + 1) or (e^x + 1). So the area is pi (e^x + 1) ^2. The area of the inner disk is pi (2)^2. Subtract the inner area from the outer and multiply by dx to get volume and integrate from 0 to 2. You will get answer 4.