Science:Math Exam Resources/Courses/MATH103/April 2005/Question 01 (d)
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Question 01 (d) 

Multiple Choice Question: Select ONE correct answer (i), (ii), (iii), (iv), or (v). (d) The value of the integral is

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 integration by parts. 
Hint 2 

Let . 
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. Simple substitution does not work in this problem, so we will need to integrate by parts. Let and . Then and . Thus,
Evaluating the definite integral then gives
Therefore, the correct answer is (i). 