Double integration 3

["Dr. Takashi Kikuchi" <takashi.kikuchi@st-hughs.oxford.ac.uk>]

Dear All

After several try and error, I have found a solution for a double
integration of  f(x,y)= 2- 2*x- 2*y/3 over {x, 0,1} and {y, 3-x, 3-3x}.
Integrate on y first and on x next.

 demo.fn <- function()
{
 fun <- function(x)
 unlist(lapply(x, function(x)
 {
  integrate(f = function(y, x)
  2 - 2 * x - (2 * y)/3, lower = 3 - x, upper = 3 - 3 * x, x = x)$integral
 }
 ))
 integrate(f = fun, lower = 0, upper = 1)$integral
}

 demo.fn()
[1] 0.4444444

This returns "a right answer". Does it have something wrong? Please test
these S-codes with your examples and report it.
Thank you.

Best,
Takashi Kikuchi