If the domain isn't specified, the question is incomplete (of course if G factorizes, the integral does, too)! Once that's been specified, this presentation Article Introduction To Monte Carlo Algorithms
i am really thankful for your answer really appreciate it . and also yes the the question was incomplete and later found the complete one with conditions and details about domain .......@Stam_Nicolis
I am not sure about your domain but double integral is nearly same as normal integral. You are in three dimensions only. You take random numbers for (x,y,z) and check it for exp(x).y