Science:Math Exam Resources/Courses/MATH103/April 2010/Question 05 (a)
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Question 05 (a) 

In this problem, you are asked to find a value for the integral in two different ways. (a) Use one of the integration techniques to compute the above integral directly. (Leave your answer in terms of sines and cosines of some number.) 
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 

Products of functions usually fall victim to integration by parts. 
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. Let and . This gives and . Hence, using integration by parts, we have
completing the problem. 