Two Algorithms for Monte Carlo Integrals Model

What is this model?

This systems model estimates the value of an integral by finding the average value of a function over a specified domain. Upon user direction, the excel sheet will generate random numbers within the domain of the first quadrant of a unit circle. These numbers will then be used to find the average value of the function (y-value) and, after multiplying by four, provide an estimate for pi. From this model, students should learn how to calculate the value an integral without algorithmic methods, but rather with experimental and computational methods.

What can this Model be used to teach?

Learn how to use random numbers and the average value of a function to approximate the integral of an unintegratable equation

Learn how to use random number and a unit square to approximate the integral of an unintegratable equation

Understand the Law of Large Numbers and how an increased number of trials yields improved accuracy

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