Find the volume generated by rotating the given region over x=1.
http://i344.photobucket.com/albums/p335/HMV99/graph.jpg
Find the volume generated by rotating the given region over x=1.
http://i344.photobucket.com/albums/p335/HMV99/graph.jpg
using washers w/r to y ...
$\displaystyle V = \pi \int_0^1 1^2 - (1-y)^2 \, dy$
using cylindrical shells w/r to x ...
$\displaystyle V = 2\pi \int_0^1 (1-x)(1-x) \, dx$
or w/o calculus ...
volume of cylinder - volume of cone
$\displaystyle \pi r^2 h - \frac{\pi}{3} r^2 h = \frac{2\pi}{3} r^2 h$
r = 1, h = 1