Science:Math Exam Resources/Courses/MATH101/April 2011/Question 04 (a)
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Question 04 (a) 

Evaluate the integral (hint: put ). 
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 

If , then . 
Hint 2 

Use partial fractions. 
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Solution 

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Please rate my easiness! It's fun and helps everyone guide their studies. Set the following change of variable then we have and so Making this substitution in the integral gives Now we use the method of partial fractions. We have We want to find numbers and such that Multiplying both sides by yields Equating coefficients of powers of on both sides gives From the first of these equations we see that . So the second equation becomes Hence and . Therefore, we have Using this to rewrite the last integral above, we find 
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