Two-Dimensional Integrals Using the Monte Carlo Method

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Consider the family of surfaces defined by , where . This Demonstration plots the surface and approximates the two-dimensional integral , the volume under the surface, using a Monte Carlo approximation method. You can vary the values of the parameters , , and and the number of randomly generated points on the surface. The approximate volume, given by , is compared to the result from Mathematica's built-in function NIntegrate.

Contributed by: Housam Binous, Brian G. Higgins, and Ahmed Bellagi (May 2013)
Open content licensed under CC BY-NC-SA


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