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Students and Mathematica: Using a Monte Carlo Method for Definite Integration

S. Keltner
S. Sloan

Leon Hall
Journal / Anthology

Mathematica in Education
Year: 1994
Volume: 3
Issue: 1
Page range: 31-33

During our second semester calculus class, we learned about many types of integration. After learning about integrating by using antiderivatives, we explored numerical integration with the Trapezoid Method and Simpson's Rule. Our professor mentioned that it would be possible to evaluate definite integrals by generating random points and determining whether or not they fell under the area of the function. He said that a Mathematica program could be created that would perform the operations. We were very interested in exploring the idea of using a Monte Carlo method to evaluate definite integrals. Since we wanted to test the accuracy and precision of the method, it was necessary to design a program that would perform the procedure several times with varying numbers of random points for each calculation.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Calculus
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KeltnerFigures.nb (49.7 KB) - Figures from article in EPS format
MonteCarlo.nb (42.6 KB) - Mathematica Notebook

Files specific to Mathematica 2.2 version:
KeltnerFigures.ma (20.4 KB) - Figures from article in EPS format
MonteCarlo.ma (29.8 KB) - Mathematica Notebook 2.2 or older