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Integration problem : Beta function related

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data

    the problem is in the figure

    2. Relevant equations

    beta function = ∫u^x-1 * (1-u)^y-1 du " the integral is form 0 to 1"

    3. The attempt at a solution

    to use the beta function the integral must be from 0 to 1 but this problem is from 0 to a
    so i let X^2=a^2 * t
    and i got from it x, dx . the integral became from 0 to 1 and everything seemed fine till i found that the (1-x)^0.5 will be (1-a root t)^0.5 which isn't the general forum of the beta function. so i hope any1 will help me or tell me if there's another way to solve this integral without the beta function if it's possible
     

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  3. Jan 16, 2012 #2

    Dick

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    You could just do the u-substitution u=1-x. So just expand x^4=(1-u)^4 and integrate term by term.
     
  4. Jan 16, 2012 #3

    hmm ty for this answer it worked out well.but don't u know any solution for it by using beta function since the problem in the book was after that lesson
     
  5. Jan 16, 2012 #4

    Dick

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    Well, your original integral is an 'incomplete beta function' if that's what your are after.
     
  6. Jan 18, 2012 #5
    yea i figured that after awhile. anyway thanks alot for your help
     
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