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I cannot prove that the integral is 0

  • Thread starter dirk_mec1
  • Start date
  • #1
761
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Homework Statement


Evaluate

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

Homework Equations


hint: the integral is zero.


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.
 
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Answers and Replies

  • #2
Dick
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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:
  • #3
761
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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.
The integral is in stewart's book problem plus section I very much doubt that the beta function needs to be invoked...
 
  • #4
Dick
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The integral is in stewart's book problem plus section I very much doubt that the beta function needs to be invoked...
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'.
 
  • #5
Cyosis
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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].
 
  • #6
Dick
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26,258
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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].
Nice observation!
 
  • #7
761
13


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].
This is what I've been waiting for.
 

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