Find the volume generated by rotating the given region over x=1.
http://i344.photobucket.com/albums/p335/HMV99/graph.jpg

2. using washers w/r to y ...

$V = \pi \int_0^1 1^2 - (1-y)^2 \, dy$

using cylindrical shells w/r to x ...

$V = 2\pi \int_0^1 (1-x)(1-x) \, dx$

or w/o calculus ...

volume of cylinder - volume of cone

$\pi r^2 h - \frac{\pi}{3} r^2 h = \frac{2\pi}{3} r^2 h$

r = 1, h = 1