Numerical Integration over 2 to 20 dimensions

Hello,

In program I'm working on, the input from the user is inline function v( a ) with number of variables (max 20) so I get function v( a1 ,..., an ) and point x .

Then I use that function to compute vector I , which is defined like this:

I succesfully computed this for 2 variables where v(a1,a2) = max(a1 + a2 - 1,0) and some given x and then I used integral2 to integrate wrt a1 and a2 but I don't know how to solve this for let's say 4 or more variables, cuz theres no integral4 or higher. It all depends how many variables the function v(a) has.

So if anyone could push me in the right direction I would appreciate it.

Thank you.