Monte Carlo Integration

by Ines Said

Submitted : Fall 2016

Calculating different areas and volumes of regular shapes is usually easy and can be done quickly. However, calculating the areas of irregular shapes such as areas under curves is significantly more difficult. Integrals are usually used to solve such problems. If the function of the curve is not too complicated, the integrals would be relatively easier to solve, but once the function gets complicated or the integral gets higher dimensions, it would be easier to refer to another way of solving integrals. Monte Carlo Integration is a method that could be used to solve more complicated definite integrals in an easier way than the normal usual way of analytically solving an integral. It uses randomly generated points, compares their location to the points of a function, rejects the unnecessary points and estimate a result for the integration. This project explains how to perform Monte Carlo Integration step by step with the help of a computer program (in Appendix) and proves that Monte Carlo Integration and normal analytically solving of integrals give the same result.

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