Science:Math Exam Resources/Courses/MATH101/April 2013/Question 01 (c)
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Question 01 (c) 

ShortAnswer Questions. Question 13 are shortanswer questions. Put your answer in the box provided. Simplify your answer as much as possible. Full Marks will be awarded for a correct answer placed in the box. Show your work, for part marks. Evaluate 
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 

The integrand is a fraction of polynomials. What integration technique is ideal for this situation? 
Hint 2 

Try partial fractions! 
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. This is a rational function, so we try partial fractions. The integrand's denominator can be factored, then we apply partial fraction decomposition giving Cross multiplying, We can solve this several ways. (1) Setting we get , and setting we get , so . (2) Comparing coefficients of the constant term, we get , and then comparing coefficients of the term, we get , so . (3) We get and by inspection. Now we solve the integral: The answer is equivalent. 