double integration in R with additional argument

Question

I learned in this question calculating double integrals in R quickly how to do double integral.

My problem is when there is one more argument of the function. Please see the example.

z = 2
fun0 = function(x,y) { tan(x+y)*z }
fun01 = integrate(function(y) { 
   sapply(y, function(y) {
      integrate(function(x) fun0(x,y), -.5, y)$value
   })
}, 0, .5)$value

The result is as follows.

 > fun01
[1] 0.1447771

I would like to make this 'fun01' to a function of z.

Answer 1

How about this

fun0 = function(x,y,z) { tan(x+y)*z }
fun01 <- function(z) {
    integrate(function(y) { 
        sapply(y, function(y) {
            integrate(function(x) fun0(x,y,z), -.5, y)$value
        })
    }, 0, .5)$value
}

fun01(2)

Just take the z out of the global environment and pass it thought where you need it.

Answer 2

Just after posting this question, I think I found the answer.

fun0 = function(x,y,z) { tan(x+y)*z }
fun01 = function(z) {
  integrate(function(y,z) {
    sapply(y, function(y) {
      integrate(function(x,z) fun0(x,y,z), -.5, y, z=z)$value
    })
  }, 0, .5, z=z )$value
}

It works as follows.

> fun01(2)
[1] 0.1447771
> fun01(3)
[1] 0.2171656