Science:Math Exam Resources/Courses/MATH103/April 2010/Question 01 (b)
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Question 01 (b) |
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Multiple Choice Question: Exactly ONE of the answers provided is correct. There is no partial credit in this questions. To find the integral using integration by parts, the best choice for u and dv in the first step would be |
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 |
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You can either try each case or try to guess what would happen if you tried each case without actually writing each. |
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. We want to integrate with integration by parts. We have three possible products:
b) c)
The second product also doesn't make sense because the second term is not easy to integrate. Also choosing as and as is not good since integrating AND derivating makes the equation more complicated. So it must be the third product. It doesn't matter, if we choose as or because the integral is the same (excapt for constants). If we choose as , we get as , what makes the equation more complicated. So we take as and get and and get . That simplified the equation. So we take answer ii. Integration would work now like this: |