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Integration, U substitution help

  1. Jul 22, 2011 #1
    1. The problem statement, all variables and given/known data

    Hi I am having a few problems with the below u substitution can anyone help,
    In particular what to do with the integral of the u substitution?

    2. Relevant equations

    [itex]\int[/itex]2x2 square root of 1-x3 dx, u = 1-x3

    Any pointers would be appreciated
    Thanks
    D
     
  2. jcsd
  3. Jul 22, 2011 #2
    Once you have u just take the derivative of it and substitute it back in for dx. The u is right and I can see that it will work out just fine. Try reviewing an example from your notes or the textbook.
     
  4. Jul 23, 2011 #3
    Can you show us the work you've done so far?
    The next step is to find du/dx.
    Create something in the integral which we can replace (...)dx and put in du.
    Can you show what you get for du/dx?

    Please read the section on https://www.physicsforums.com/showthread.php?t=414380"
     
    Last edited by a moderator: Apr 26, 2017
  5. Jul 23, 2011 #4
    Hi Thanks for the help much appriciated,

    I think I have worked it out, answer below;

    -4/9(1-x3)3/2 du?

    I have differentiated it and I get back to original answer.

    Just one thing, if my original limits were 2,1 would my new limits be -7,0?

    Thanks again
    Dominic
     
  6. Jul 23, 2011 #5
    You got it except you don't need the du at the end. And actually you need your +C as well. But I don't know what you mean with your question regarding limits.
     
  7. Jul 23, 2011 #6
    Yes, that's right.
    Check your answer here
    A word of caution about that site- use it only to check your work, or help you through a particularly difficult integral. It's too easy to put it in there first & think one is learning.

    When to drop the du?
    When one actually does the integral operation. Both the integral sign & du disappear on the same step, when one does the integral itself, after the prep. work(substituting u, constant multipliers, etc.) but before evaluating a definite integral.

    About +C, stengah is half right. Without limits of integration it needs a +C. Of course with limits of integration drop the +C.

    When you do a definite integral with limits of integration, 2 & 1, the new limits of integration would be -7 & 0. The convention is to mention the bottom limit first, because if you see it graphically, the bottom number is on the left.
     
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