Monte-Carlo Integration is a numerical method of taking the integral $\int_X f(x) dx$ by sampling $x_1,\ldots,x_N \in X \subseteq \mathbb{R}^n$, and then averaging $I_N = \text{Vol}(X) \sum_{i=1}^N f(x_i)$. By the law of large numbers $I_N \to I$ with $N \to \infty$. See also http://en.wikipedia.org/wiki/Monte_Carlo_integration.