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Math Help - Integrals/Substitution help.

  1. #1
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    Integrals/Substitution help.

    Hi,

    My math is really rusty and i need to do the following double integral for a statistics problem.

    so the simplified double integral goes something like this:

    integral (1, 0) integral (1-x2, 0) ([c(x1^a1-1)(x2^a2-1)(1-x1-x2)^a3-1 dx1 dx2])

    c is a constant.

    now the hint says perform the following substitution:

    u = x1/1-x2.
    thus du = (1-x2)^-1 (dx1)

    now i don't know what we do with the dx2 in the equation. I performed the substitution and basically, x2 = 1 - (x1/u). so all the x2's are gone in the equation and we are left with that. Shouldn't we get rid of dx2 somehow? I need help with that.
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  2. #2
    MHF Contributor
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    What is this supposed to look like? Let \displaystyle x_1=x, \ x_2=y, \ a_1=a, \ a_2=b, \ a_3=c, \ c=k

    \displaystyle k\int_{0}^{1}\int_{0}^{1-y}(x^a-1)(y^b-1)(1-x-y)^cdxdy

    Is this what you are trying to solve?
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