I am trying to evalute this integral: $$ \int_{A} x^{m} y^{n} z^{p}(1-x-y-z)^{q}|d x \wedge d y \wedge d z| $$
A=R3 , x , y and z are positive and x+y+z<=1
I used the change of values u=x+y+z , v=(z+y)/u and $\omega$=z/(y+z) which gave me x=u(1-v) y=vu(1-$\omega$) and z=uv$\omega$
The det of the matrix of the change of variables is: u^2*v
However, I am struggling to find the boundries for u, v and $\omega$ and carrying the calculation.
Any help would be appreciated.