r - How to pass vector to integrate function

Question

I want to integrate a function fun_integrate that has a vector vec as an input parameter:

fun_integrate <- function(x, vec) { 
  y <- sum(x > vec)
  dnorm(x) + y
}

#Works like a charm
fun_integrate(0, rnorm(100))

integrate(fun_integrate, upper = 3, lower = -3, vec = rnorm(100))
300.9973 with absolute error < 9.3e-07
Warning message:
  In x > vec :
  longer object length is not a multiple of shorter object length

As far as I can see, the problem is the following: integrate calls fun_integrate for a vector of x that it computes based on upper and lower. This vectorized call seems not to work with another vector being passed as an additional argument. What I want is that integrate calls fun_integrate for each x that it computes internally and compares that single x to the vector vec and I'm pretty sure my above code doesn't do that.

I know that I could implement an integration routine myself, i.e. compute nodes between lower and upper and evaluate the function on each node separately. But that wouldn't be my preferred solution.

Also note that I checked Vectorize, but this seems to apply to a different problem, namely that the function doesn't accept a vector for x. My problem is that I want an additional vector as an argument.

Answer 1

integrate(Vectorize(fun_integrate,vectorize.args='x'), upper = 3, lower = -3, vec = rnorm(100),subdivisions=10000)

304.2768 with absolute error < 0.013


#testing with an easier function
test<-function(x,y) {
  sum(x-y)
}

test(1,c(0,0))
[1] 2

test(1:5,c(0,0))
[1] 15
Warning message:
In x - y : 
longer object length is not a multiple of shorter object length

Vectorize(test,vectorize.args='x')(1:5,c(0,0))
[1]  2  4  6  8 10

#with y=c(0,0) this is f(x)=2x and the integral easy to solve
integrate(Vectorize(test,vectorize.args='x'),1,2,y=c(0,0))
3 with absolute error < 3.3e-14 #which is correct