Moment of a distribution

dipole

I have the following equation, and I'm trying to understand it. The k^th moment of a distribution can be approximated as follows:

[tex] \frac{1}{N}\sum_{i=1}^N{x_i^k} \approx \int{x^kP(x)dx} + O(1/\sqrt{N}) [/tex]

Where [itex] P(x) [/itex] is the probability distribution.

I understand where the integral comes in, but I don't understand how to quantify the error in the approximation as [itex] O(1/\sqrt{N}) [/itex].

Can someone help explain how to derive this? Thanks.