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Need help trying to integrate a messy function

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data
    Evaulate the following integral:
    2*integral from r-b to r of h(x-r+b)b*sqrt(r2-x2) dx
    or a picture
    http://imgur.com/n2PUN

    2. Relevant equations



    3. The attempt at a solution

    Tried setting u = r^2-x^2, lost after a couple more steps. Nothing seems to cancel out smoothly. For the record, Im in Calc II, and have not learned integral by parts or trig sub.
    Heres a webpage I got the integral from http://mathworld.wolfram.com/CylindricalWedge.html
     
    Last edited: Feb 12, 2012
  2. jcsd
  3. Feb 12, 2012 #2
    I assume r, b, and h are constants. If so, split the integral into
    [itex]2\displaystyle\int\limits_{r-b}^r \dfrac{hx}{b} \sqrt{r^2 - x^2} dx + 2\int\limits_{r-b}^r \frac{h(b-r)}{b} \sqrt{r^2 - x^2} dx[/itex]

    Then the first can be done with the substitution you've tried already, and the second will require a trig substitution.
     
  4. Feb 12, 2012 #3
    Thank you, worked it out and will ask the professor tomorrow. Thanks for your help!
     
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