MATH103 April 2010
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q2 • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 •
Question 01 (b)
Multiple Choice Question: Exactly ONE of the answers provided is correct. There is no partial credit in this questions.
To find the integral
using integration by parts, the best choice for u and dv in the first step would be
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!
You can either try each case or try to guess what would happen if you tried each case without actually writing each.
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.
- If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
- If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.
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 want to integrate
with integration by parts. We have three possible products:
The first product doesn't make sense to choose since the second term is neither easy to derivate nor to integrate.
The second product also doesn't make sense because the second term is not easy to integrate. Also choosing as and as is not good since integrating AND derivating makes the equation more complicated.
So it must be the third product. It doesn't matter, if we choose as or because the integral is the same (excapt for constants). If we choose as , we get as , what makes the equation more complicated.
So we take as and get and and get . That simplified the equation. So we take answer ii.
Integration would work now like this:
Click here for similar questions
MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Integration by parts, Pages using DynamicPageList parser function, Pages using DynamicPageList parser tag