[R] efficiently finding the integrals of a sequence of functions

[JeffND]

Hi folks,

I am having a question about efficiently finding the integrals of a list of
functions. To be specific,
here is a simple example showing my question.

Suppose we have a function f defined by

f<-function(x,y,z) c(x,y^2,z^3) 

Thus, f is actually corresponding to three uni-dimensional functions
f_1(x)=x, f_2(y)=y^2 and f_3(z)=z^3.
What I am looking for are the integrals of these three functions f_1,f_2,f_3
over some interval, say, (0,1).
More specifically, the integrals \int_0^1 f_1(x) dx, \int_0^1 f_2(y) dy and
\int_0^1 f_3(z) dz.

For this simple example, of course we can do these three integrals one by
one using

integrate (f_1, lower=0, upper=1)

However, in practice, I have a sequence of 5000 uni-dimensional functions
and hope to find all of their 
integrals (over some regions), so using loops to do this one by one is not
efficient. 

A possible idea is to convert the sequence of functions to a list of
objects, and use sapply()
which allow us to find the integrals in a fashion of vectorizing. But I
don't know how to convert
the above example function f to a list. In my research problem, I can only
define the 5000 functions
in a vectorizing way like

f<-function(x1,x2,...,x5000) c(f1(x1),f2(x2),...,f5000(x5000))

So how to convert it to a list will be a crucial step to efficiently get the
integrals.

Thanks for all the suggestions!
Jeff




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