Given a random variable with probability density function f(x), how to compute the expected value of this random variable in R?

If you want to compute the expected value, just compute :

E(X) = Integral of xf(x)dx over the whole domain of X.

The integration can easily be done using the function integrate().

Say you're having a normal density function (you can easily define your own density function) :

f <- function(x){
     1/sqrt(2*pi)*exp((-1/2)*x^2)
}

You calculate the expected value simply by:

f2 <- function(x){x*f(x)}
integrate(f2,-Inf,Inf )

Pay attention, sometimes you need to use Vectorize() for your function. This is necessary to get integrate to work. For more info, see the help pages of integrate() and Vectorize().