Question 04 (c)
Compute the following integrals. (Leave your answers in terms of or .)
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!
The factored bottom should make partial fractions a natural choice for a technique to attempt this problem.
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.
We proceed by partial fractions. Let A and B be constants such that
Since the denominators are the same, the numerators must be equal and hence
Now, since this equality holds for all values of x, we can plug in specific values for x to get the coefficients. At , we have
and so . At , we have
and so . Hence, we have