# How do you find the volume of the solid generated by revolving the region bounded by the curves x=y-y^2 rotated about the y-axis?

##### 1 Answer

Oct 26, 2015

See the explanation section below.

#### Explanation:

Here is a picture of the region with a representative slice taken perpendicular to the axis of rotation. This is a set-up to use disks to find the volume. The thickness is

As

The volume of the representative disk is

So, to find the volume of the solid, we need to evaluate

This integral evaluates to

**Bonus**

Here is a link to the same volume problem using shells instead of disks.