In Chapter 5, we implemented an Octave function `mcintgr`

and its vectorized version `mcintgrv.`

This function can evaluate the integral for a mathematical function *f* in some interval [*a*; *b*] where the function is positive. The Octave function is based on the Monte Carlo method and the return value, that is, the integral, is therefore a stochastic variable. When we calculate a given integral, we should as a minimum present the result as a mean or another appropriate measure of a central value together with an associated statistical uncertainty. This is true for any other stochastic variable, whether it is the height of the pupils in class, length of a plant's leaves, and so on.

In this section, we will use Octave for the ...

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