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Question 8 (b) 

Let be the region to the right of the axis that is bounded by the graphs of and . Both parts of this question concern this region . (b) Write down an expression, using horizontal slices (disks), for the volume obtained when the region is rotated around the axis. Do not evaluate any integrals; simply write down an expression for the volume (you don’t need to justify it). 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Disc method of integration 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We solve for in both equations, yielding and . The two curves intersect at , and so two integrals are needed: for the radius of the disc is , while for the radius of the disc is . The total volume is therefore
