1. ## 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.

2. 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?