How to supply a function elementwise to Integral2

Hi guys,

I want to evaluate a double integral of the form int_{-inf}^a int_{-inf}^b sum_{i,j}^K a_i*a_j*x^i*y^j*exp(-x^2 - y^2 + x*y)dx dy where a_i and a_j are constants. Since the integral is linear, I can change summation and integration, but in this case I have to evaluate K^2 integrals and it takes too long. In that case I do the following:

for i = 1:K
   for j = 1:K
       fun = @(x,y) x.^i.*y.^j.*exp(-2.*(x.^2 + y.^2 - 2.*x.*y))
       part(i,j) = alpha(i)*alpha(j)*integral2(fun,-inf,a,-inf,b)
   end
end

It takes too long, so I want to evaluate only one integral, but I don't know how to factorize sum_{i,j}^K a_i*a_j*x^i*y^j*exp(-x^2 - y^2 + x*y), namely, how to supply it to integral2. | would be very grateful for any help.

Kind regards, Renata