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Help with trigonometric substitution

  1. Feb 22, 2013 #1
    1. The problem statement, all variables and given/known data

    integral (1)/(x^2sqrt(36-x^2)

    2. Relevant equations



    3. The attempt at a solution
    I found X=6sinθ dx=6cos
    √(36-x^2)=√(36-sin^2θ)=6cosθ
    i think the problem is that i am not getting integral of ∫csc^2θ
     
  2. jcsd
  3. Feb 22, 2013 #2

    Dick

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    You should. Show the rest of your work so someone can tell you where you went wrong.
     
  4. Feb 22, 2013 #3
    i know the answer which is -√(36-x^2)/36x+C
     
  5. Feb 22, 2013 #4

    Dick

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    That's not the rest of your work, that's what I asked for. You've got a cos(θ) and the numerator and cos(θ) in the denominator. They cancel. What's left?
     
  6. Feb 22, 2013 #5
    The integral is -cotθ + C
     
  7. Feb 22, 2013 #6

    Dick

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    That's part of it. There's also a constant around. But like we were talking about in your last post there is a way to express -cot(arcsin(x/6)) as a function of x without any trig functions. That's what the books answer is.
     
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