Project 10 considers the problem of approximating the integral of a function over a multidimensional domain in cases where a formula or exact value cannot be produced. In such cases, the Monte Carlo method provides a way of producing approximate results.
The case study presents two ways of looking at the Monte Carlo method. In the first case, we recall that integration is equivalent to computing the area under a curve - a concept which extends to the multidimensional case as approximating a volume.
In the second view, we think of integration as a way of computing the average value of a function over the integration domain (if we divide the integral by the area of the domain). This approach helps us to get some additional information from the Monte Carlo method, which can suggest to us whether our approximation is probably good enough for our purposes.
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