Question: double integral

Hello,
I am trying to do the following double integral in tranches as listed here:

P := proc (x, y) options operator, arrow; (1/2)*exp(-(1/2)*(x^2+G*y^2-2*B*x*y)/(-B^2+G))/(Pi*sqrt(-B^2+G)) end proc

Since G and B are constant

((int(x = 0 .. infinity))*(int(y = -infinity .. 0))+(int(x = -infinity .. 0))*(int(y = 0 .. infinity)))*P(x, y)

But does notwork. How do I pass these coordinates to polar?

Regards.

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