Science:Math Exam Resources/Courses/MATH101/April 2006/Question 03 (b)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q1 (i) • Q1 (j) • Q1 (k) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 (a) • Q4 (b) • Q5 • Q6 • Q7 •
Question 03 (b) 

FullSolution Problems. Justify your answers and show all your work. Simplification of answers is not required. Evaluate the following 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 integrating by partial fractions. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We proceed by partial fractions. Let
where above we used the fact that is irreducible (its discriminant is ). Thus, we know that
Plugging in gives
and so . Plugging in gives
and so . Plugging in gives
and so . Adding the last two equations and dividing by 2 gives and so Hence, we have
To solve the last integral, use substitution. Let so that and so
and so
