Consider the problem of finding the area under the curve between x = 0 and x = 2:
Even if you know calculus, this is a difficult task. However, a relatively simple idea will allow us to approximate the area.
The idea begins with putting a box around the graph that contains it completely. For a function that stays positive, this means finding a maximum value m; in this case, we can use m = 1:
Now imagine throwing random ...