Performing numerical integration using Monte Carlo

Monte Carlo simulations represent a numerical solution for calculating integrals. In fact, with the use of the Monte Carlo algorithm, it is possible to adopt a numerical procedure for the solution of mathematical problems, with many variables that do not present an analytical solution. The efficiency of the numerical solution increases compared to other methods when the size of the problem increases.

Important Note

Let's analyze the problem of a definite integral. In the simplest cases, there are methods for integration that foresee the use of techniques such as integration by parts, integration by replacement, and so on. In more complex situations, however, it is necessary to adopt numerical procedures that involve the use of a computer. In these cases, the Monte Carlo simulation provides a simple solution that's particularly useful in cases of multidimensional integrals.

However, it is important to highlight that...