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Question 01 (e) 

Calculate the volume of the solid obtained by rotating the region above the xaxis, below the curve and between the lines and about the yaxis. 
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 

Use the method of cylindrical shells. (Shell 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. To solve this question, choose an x between and . From here, the radius of a shell rotated about the yaxis is just r = x and the height of this shell is . The distance the height travels aroudn the yaxis is and hence, we have
