Triple integration using R when each inner integral depends on the others

Question

My question is similar to "double integral in R.", but in my case, I want to do a triple integration where each limit depends on the outer integral.

I wnat to calculate

How do I define the inner dependencies?

Answer 1

I think, that basing on the suggestion from the post you have attached the key is to add the Vectorize function and we come up with something like this:

# Example function 
phi <- function(t){t}

integrate(Vectorize(function(x) { 
  integrate(Vectorize(function(y) { 
    integrate(function(z) { 
      phi(x)*phi(y)*phi(z)   ## function you want to calculate
    }, -10, 6-x-y)$value     ## 2nd level interval
   }), -5, 3-x)$value        ## 1st level interval
}), -5,4)                    ## top interval

# 16480.2 with absolute error < 1.8e-10

the above approach is quite general, so you can test on other functions. (The answer is the same as provided by WolframAlpha)