Science:Math Exam Resources/Courses/MATH101/April 2008/Question 01 (c)
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Question 01 (c) 

Express as a definite integral. Do not evaluate the 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 

This is a Riemann sum. Recall that and that Then do a pattern match. 
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. From the question, we immediately see that Now, to determine , notice that we have that the function is of the form The only composition of functions is underneath the square sign. So we must have that and hence that As , we have that and hence since we have that . Combining the above gives which completes the question. 