How do you find the volume of the region enclosed by the curves y=x, y=-x, and x=1 rotated about y=1?

1 Answer
Aug 27, 2015

The volume is 2pi

Explanation:

Using the method of washers

Let the outer radius be 1-(-x)=1+x

Let the inner radius be 1-x

The integral for the volume is

piint_0^1(1+x)^2-(1-x)^2dx

piint_0^1(1+2x+x^2)-(1-2x+x^2)dx

piint_0^1(1+2x+x^2-1+2x-x^2)dx

piint_0^1(4x)dx

Integrating we get

2pix^2

Evaluating from 0 to 1

2pi(1)^2-0=2pi