Possible infinite loop on math equation?

Question

I have the following problem, and am having trouble understanding part of the equation:

Monte Carlo methods to estimate an integral is basically, take a lot of random samples and determined a weighted average. For example, the integral of f(x) can be estimated from N independent random samples x_r by

alt text http://www.goftam.com/images/area.gif

for a uniform probability distribution of xr in the range [x1, x2]. Since each function evaluation f(xr) is independent, it is easy to distribute this work over a set of processes.

What I don't understand is what f(x_r) is supposed to do? Does it feed back into the same equation? Wouldn't that be an infinite loop?

Answer 1

It should say f(x_i)

f() is the function we are trying to integrate via the numerical monte carlo method, which estimates an integral (and its error) by evaluating randomly choosen points from the integration region.

Ref.