Science:Math Exam Resources/Courses/MATH105/April 2018/Question 02 (d)
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Question 02 (d) 

Evaluate where . 
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 

Apply the substitution . 
Hint 2 

After applying the substitution in Hint 1, use integration by parts to evaluate the integral. 
Hint 3 

In order to evaluate integral, use a substitution if it's needed. 
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. Use a substitution . Then, we have , , and
Here, and are used.
Then, we apply the integration by parts for , , , and in
to get
Using the substitution , we get Plugging this, we can evaluate the given integral as Answer: 