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Integration (by parts) check my work

  1. Mar 20, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex]\int x^2*cosx dx[/tex]

    2. Relevant equations

    3. The attempt at a solution

    Okay, so I started by making...

    Then I made the rudimentary equation:

    [tex]\int x^2 * cos(x) dx = -x^2*sin(x) + \int 2x * sin(x) dx[/tex]

    Then I took the last integration problem (the one all the way on the right) and did integration by parts on that one again, to make:


    to make...

    [tex]\int x^2 * cos(x) dx = -x^2 * sin(x) + 2x * sin(x) + \int 2 * cos(x) dx[/tex]

    I evaluated the last integration problem to be -2*sin(x), and got a final answer of sin(x)(-x^2+2x-2) (after factoring). Of course, my calculator says this is wrong, so where'd I mess up?

    Thanks. (I'm getting better with Latex, btw)
    Last edited: Mar 20, 2007
  2. jcsd
  3. Mar 20, 2007 #2


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    Staff Emeritus
    Science Advisor

    In your first step, if dv=cos(x)dx, then v=sin(x) (no minus sign).
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