A Concise Introduction to Programming in Python

Chapter 10

Simulation

Consider the problem of finding the area under the curve f(x) = e

−x

2

between

x = 0 and x = 2:

0.5

1.0

1.5

2.0

0.2

0.4

0.6

0.8

1.0

Figure 10.1: Graph of f(x) = e

−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 com-

pletely. For a function that stays positive, this means finding a maximum value

m; in this case, we can use m = 1:

0.5

1.0

1.5

2.0

0.2

0.4

0.6

0.8

1.0

Figure 10.2: Box containing area.

Now imagine throwing random darts into the box. Some will land below the

graph, in the area we want to measure, ...