Science:Math Exam Resources/Courses/MATH101/April 2007/Question 01 (c)
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Question 01 (c) 

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 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 

This is a Riemann sum problem. Try isolating a factor of 
Hint 2 

The values should look like
and so
See if you can determine the rest of the values. 
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. Notice that our question is equivalent to
The values for the Riemann sum look like
and so
and so with the above in the , we can deduce that
and our function should be
Hence, we have
completing the question. 