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Question 02 (c) 

FullSolution Problem. Justify your answers and show all your work. Simplification of answers is not required. Set up, but do not evaluate, a definite integral for the volume of the solid obtained by rotating the region between and for about the line . 
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 

It might help to draw a picture. 
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. A picture is included below. Imagine yourself standing on the xaxis at x=1 looking towards the rotated object. This top down view (the circles in the picture) show that what we are doing is taking a cylinder of radius 1 and height , and subtracting from it the shape that we get from removing the inner shape of radius . This gives the volume to be
completing the question. 