Monte Carlo Integration

Definition

${\int }_a^{b}h(x)dx={\int }_a^{b}q(x)f(x)dx=E[q(X)]\approx \frac{1}{n}\sum _{i=1}^{n}q(X_i)$ where $h(x):=q(x)f(x)$ and $f(x)$ is a PDF