# Volumes of solids of revolutions

• January 27th 2009, 05:57 PM
nystudent2729
Volumes of solids of revolutions
Find the volume of the solid obtained by rotating the region bounded by the graphs of y=x^(2) and x=y^(2) around the line x=-1.
Thanks for the help.
• January 27th 2009, 06:08 PM
skeeter
using cylindrical shells w/r to x ...

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

using washers w/r to y ...

$V = \pi \int_0^1 (\sqrt{y} + 1)^2 - (y^2 + 1)^2 \, dy$