I'm working in R and I would like to know if it is possible to create a function f(x) obtained from an integral of a function g(x,y) with respect to the variable y for example in (0,1), lets say:
I tried this code
f <- function(x){integrate(function(y){g(x,y),0, 1)}
(with g(x,y) an explicit function) but it didn't work unless I fixed x.
Also some help with formatting would be awesome since this is unreadable! Thanks!
It is avaiable. You can try
f <- function(x,y) x + y
f(1,2)
it <- function(x) {
g <- function(y) f(x,y)
integrate(g, 0,1)
}
it(1)
{caracas} might be what you're looking for. Here is a reproducible example:
library(reticulate)
library(caracas)
# make symbols x and y:
x <- symbol("x")
y <- symbol("y")
Function g:
g <- x ** 3 - y ** 3
g
#> [caracas]: 3 3
#> x - y
Function f (integral of g w.r.t 'y' from 0 to 1):
f <- int(g, var = "y", lower = 0, upper = 1)
f
#> [caracas]: 3 1
#> x - -
#> 4
Function h (integral of f w.r.t 'x' from 0 to 1):
h <- int(f, var = "x", lower = 0, upper = 1)
h
#> [caracas]: 0
Maybe you can try this
g <- function(x, y) x^4 + y^2
f <- Vectorize(function(x) {
integrate(function(y) g(x, y), 0, 1)$value
})
and you will see
> f(c(1, 2, 3, 4))
[1] 1.333333 16.333333 81.333333 256.333333
and curve(f, 0, 5) gives
