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I cannot prove that the integral is 0

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate

    http://img338.imageshack.us/img338/4931/52219436.png [Broken]

    2. Relevant equations
    hint: the integral is zero.


    3. The attempt at a solution
    I don't know how to tackle this, can someone give me a hint please? I looked at several subsitutions and IBP's but I'm stuck.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 26, 2009 #2

    Dick

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    Re: integral

    You can evaluate the integral in terms of the Euler Beta function. Use two different substitutions for each part and properties of the gamma function to show it's zero.
     
    Last edited: Apr 26, 2009
  4. Apr 27, 2009 #3
    Re: integral

    The integral is in stewart's book problem plus section I very much doubt that the beta function needs to be invoked...
     
  5. Apr 27, 2009 #4

    Dick

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    Re: integral

    Then I would suggest you look at how the proof works in terms of the integral definition of the beta function and figure out how to do the same thing by manipulating the integrals without saying the words 'beta function'.
     
  6. Apr 29, 2009 #5

    Cyosis

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    Re: integral

    In this special case it can be done without the beta function. Note that the two given functions are each others inverses on the interval [0,1].
     
  7. Apr 29, 2009 #6

    Dick

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    Re: integral

    Nice observation!
     
  8. May 3, 2009 #7
    Re: integral

    This is what I've been waiting for.
     
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