how to speed the calculation of a double integral with monte carlo simulation

Hi All,

I´m calculating an integral with Monte Carlo Simulation (mcint.m). The function that I want to integrate is a Monte Carlo calculated integral. That´s why I get a double integral. Please look at the attached screenshot.

"A" is a set containing some y-values. y=1:6. The second integral is like a tripple integral, because x consists of x_1,x_2 and x_3. Funcations m and f: R^3->R, function g:R->R.

To use Monte Carlo I have to select the number of points and it should be 10^6, but I can´t put more than 1000 because otherwise it takes very long time (with 1000 it calculates 3 hours, with 10000 - 30 hours, more than 10000 I did not try). But to use only 1000 points is not an option because the integral is not exactly calculated then. That´s why I would like to know if there might be any possibility to speed the calculation? I attached also my code in hope, that might be useful for you to understand what I´m trying to do... In file "forum" I use Monte Carlo Simulation first time. Than in "forum1" I use the previous function to calculate the integral for different numbers y(y=1:6). And finally in "forum2" I calculate the second integral based on the set A which contains some values from y=1:6.

Thank you Best Regards xanka