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.