Volumes of Revolution

1. Dec 12, 2006

ChaoticLlama

What is the volume of the figure bounded by y = 2x - x^2, y = 2x, x = 2, and rotated about the line y = -1.

Is this the correct integral?

$$$V = \pi \int_0^2 {((2x + 1)^2 - (2x - x^2 + 1)^2 } )dx$$$