Question 04 (a)
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 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.
What seems to be complicated? Try using a substitution to get rid of the complicated part.
Try to integrate by parts now.
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.
Let so .
Cross multiplying yields .
Since , the above is equal to .
Note further that and
We integrate by parts. Let and so
completing the integral.