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## Homework Statement

The total area between a straight line

According to the book, the answer is

## Homework Equations

## The Attempt at a Solution

1. Rewrite the second equation in the form of

2. Set the two equations to each other and find which values of 'y' they intercept.

This yields the functions intercept at y= -4 and y=2

3. The

*cylindrical shells*method will be used to find the volume of revolution around the y-axis. My equation is set up to be.

4. I used Wolfram to save a bunch of Tex...my answer comes out to be

I must be approaching the problem in a wrong way but am stumped figuring out why. Any help would be greatly appreciated.