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Homework Help: Evaluate integral using substitution

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data
    evaluate using substitution
    Integral [cos^-1 x]/sqrt[1-x^2] dx

    2. Relevant equations



    3. The attempt at a solution
    I am just starting with integration and I am getting frustrated with this problem. If someone could show me how to setup and start this problem so I could attempt to continue by reading instructions from my textbook it would be greatly appreciated
     
  2. jcsd
  3. Feb 25, 2010 #2

    vela

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    Hint: What's the derivative of [itex]cos^{-1} x[/itex]?
     
  4. Feb 25, 2010 #3
    that is -1/sqrt[1-x^2] isnt it
     
  5. Feb 25, 2010 #4

    vela

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    Yup. Note that it's the other part of the integrand, so that means you should use a substitution.
     
  6. Feb 25, 2010 #5
    so u=cos^-1x. therefore du=-1/sqrt[1-x^2] dx
    is this correct so far?

    I got -[[cos^-1x]^2]/2 +c hope its right, thanks for the help
     
    Last edited: Feb 25, 2010
  7. Feb 25, 2010 #6

    vela

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    Yes, that's the correct answer. You can always differentiate what you got and see if you get back the integrand.
     
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