The present approach to the above integral is often called 'crude' or 'Brute-Force' Monte-Carlo. Later on in this chapter we will study refinements to this simple approach. The reason is that a random generator produces points that are distributed in a homogenous way in the interval $[0,1]$. If our function is peaked around certain values of $x$, we may end up sampling function values where $f(x)$ is small or near zero. Better schemes which reflect the properties of the function to be integrated are thence needed.