Computing areas and integrals with random numbers

Abstract

We introduce the basics of the Monte Carlo method that allows computing areas and definite integrals, by means of the generation of long sequences of random numbers. The areas of some nontrivial shapes are computed, showing the convergence towards their exact values. The application of the method to the computation of definite integrals is also given, showing an important example of the kinematics of a particle under the action of an arbitrary time-dependent force.