MATH101 April 2013
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 • Q9 (a) • Q9 (b) • Q10 (a) • Q10 (b) • Q11 • Q12 (a) • Q12 (b) • Q12 (c) •
Question 01 (c)
Short-Answer Questions. Question 1-3 are short-answer 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.
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.
The integrand is a fraction of polynomials. What integration technique is ideal for this situation?
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.
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This is a rational function, so we try partial fractions. The integrand's denominator can be factored, then we apply partial fraction decomposition giving
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.
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MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Partial fractions