Summary
The midpoint method of integration of a function of one variable is perhaps the simplest method of numerical integration, although it is often not mentioned in textbooks. It is here generalized to any number of dimensions and the generalization is called thecentroid method. This again is a very simple method and it can be conveniently used, for example, for the integration of a function of several variables over any non-pathological region. The numerical examples include the integration of multinormal integrands.
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Goo, I.J., Gaskins, A. The centroid method of numerical integration. Numer. Math. 16, 343–359 (1971). https://doi.org/10.1007/BF02165005
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DOI: https://doi.org/10.1007/BF02165005