007B Sample Midterm 3, Problem 4 Detailed Solution
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Find the volume of the solid obtained by rotating the region bounded by and about the axis. Sketch the graph of the region and a typical disk element.
Background Information: 

1. You can find the intersection points of two functions, say 
by setting and solving for 
2. The volume of a solid obtained by rotating an area around the axis using the washer method is given by 

where is the inner radius of the washer and is the outer radius of the washer. 
Solution:
Step 1: 

First, we need to find the intersection points of and 
To do this, we need to solve 
Squaring both sides, we get 
The solutions to this equation in the interval are 

Now, the graph of the region is below. 
Additionally, we are going to be using the washer/disk method. 
Below, we show a typically disk element. 
(Insert graph) 
Step 2: 

The volume of the solid using the disk method is 
Final Answer: 

See Step 1 for graph. 