Science:Math Exam Resources/Courses/MATH101/April 2008/Question 03 (b)
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Question 03 (b) 

FullSolution Problem. Justify your answers and show all your work. Simplification of answers is not required. Evaluate the following 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 

Note: the following hint was given on the exam. You will need to use a substitution combined with another method of integration. 
Hint 2 

Try the substution . 
Hint 3 

Integration by parts will take you home. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. As in the hint, let so that . This gives
To solve this last integral, we use integration by parts. Let
Then, we have
and hence
