Chapter 10

Consider the problem of finding the area under the curve $f(x)={e}^{-{x}^{2}}$ between x = 0 and x = 2:

Figure 10.1:

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:

Figure 10.2:

Now imagine throwing random ...

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