Science:Math Exam Resources/Courses/MATH103/April 2015/Question 10 (b)
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Question 10 (b) 

Evaluate the integral 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Use the substitution . 
Hint 2 

Apply integration by parts twice. Then, we can find the same term with in the formula. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. Using the substitution (and hence and ), we have
Then, applying the integration by parts with and , we have . and , and therefore
Applying the integration by parts one more time with and , we have
Combining these two equations, we have
so that
Finally, collecting the equations, we can evaluate as follows:
