Science:Math Exam Resources/Courses/MATH101/April 2018/Question 03 (ii)
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Question 03 (ii) 

Determine explicitly the volume of revolution obtained by rotating the bounded region between and about the axis. 
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 

Suppose that two functions and intersect at and , and satisfy on the interval . Then, the volume of revolution obtained by rotating the bounded region between and about the axis is 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. First, we find the intersection points between two curves. It is enough to solve Then, we can observe that on . (This can be done either by drawing the graphs of the two functions or by comparing the value of the two function at some point in the interval.) Note that since both functions and are even, the function is also even. Thus we have the volume Answer: 