Science:Math Exam Resources/Courses/MATH103/April 2014/Question 08 (a)
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Question 08 (a) 

Evaluate where . Your final answer should be in the form of a number. Work must be shown for full marks. Simplify fully. 
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 

Integrate termbyterm. 
Hint 2 

Write the resulting series in the form for appropriate and . 
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. Integrating termbyterm, we have
We want to use the fact that
for . To do so, write
We are thus in the situation above with and . Hence,
