Math Help - Volumes by Rotation

1. Volumes by Rotation

Find the volume of the solid that results when the region enclosed by x=y^2, and x=y is revolved about the line x=-1.

2. Originally Posted by kinana18
Find the volume of the solid that results when the region enclosed by x=y^2, and x=y is revolved about the line x=-1
most important ... sketch a diagram.

$x = y^2$ and $x = y$ intersect at $y = 0$ and $y = 1$

washers w/r to y ...

$V = \pi \int_c^d [R(y)]^2 - [r(y)]^2 \, dy$

$R(y) = y - (-1) = y + 1$

$r(y) = y^2 - (-1) = y^2 + 1$

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