# Evaluating double Integral

While trying to evaluate the integral $\int_{y=0}^{x_2}\int_{x=0}^{min(x_1,y)} n (n - 1) (1 - y)^{(n - 2)}dxdy$ , Mathematica does not seem to yield any results.

 Integrate[n (n - 1) (1 - y)^(n - 2), {y, 0, x2}, {x, 0, Min[y, x1]}]


Wolframm alpha also fails saying standard computation time exceeded. Is there anyway to evaluate the integral? I also tried this,

Assuming[0 < x1 < x2 < 1,
Integrate[n (n - 1) (1 - y)^(n - 2), {y, 0, x2}, {x, 0, Min[y, x1]}]]

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No assumptions on n? – J. M. May 20 '13 at 6:38

Hopefully we're converging on the desired integral:

Assuming[(0 < x1 < x2 < 1),
Integrate[n (n - 1) (1 - y)^(n - 2), {y, 0, x2}, {x, 0, x1}]]


(n x1 (-1 + (1 - x2)^n + x2))/(-1 + x2)


Though it may be that what you are after is:

Assuming[(0 < x1 < x2 < 1),
Integrate[n (n - 1) (1 - y)^(n - 2), {x, 0, x1}, {y, 0, x2}]]


Do you want it with or without the $n$ in the integrand? It works either way. – bill s May 20 '13 at 11:01
This is the actual integral I'm trying to evaluate: $\int_{x=0}^{x_1} \int_{y=0}^{x_2} n (n - 1) (1 - y)^{(n - 2)}dxdy$ subject to $0<x<y<1$ and $0<x_1<x_2<1$ – AIB May 20 '13 at 12:05
@AIB: You still haven't answered my question. No assumptions on $n$? BTW, you might be interested in Boole[]. – J. M. May 20 '13 at 12:09