Science:Math Exam Resources/Courses/MATH101/April 2012/Question 01 (g)
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Question 01 (g) 

ShortAnswer Question. Show all your work, simplify your answer as much as possible. Let
Express as a definite integral. Do not evaluate this 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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Try to write the sum in the form
where
and

Checking a solution serves two purposes: helping you if, after having used the hint, 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. Notice that occurs in the summand. This suggests that and so we can take . Writing the sum as
the last fraction suggests that a possible function is which can be seen by noting that we have
Also, we have
and since we have that . Combining this gives
completing the question. 