Abstract
Simpson's Rule is an accurate numerically stable method of approximating a definite integral using a quadrature with three points, obtained by integrating the unique quadratic that passes through these points. The error term in the method is a function of the fourth derivative of the integrand. Therefore, it is easy to see that the method is exact for cubics, since the fourth derivative of a cubic is zero, and there is no error. The error analysis uses Taylor series. In our simple proof, we will use ordinary integration techniques.
Citation
Rohan J. Dalpatadu. Elizabeth E. Freeman. "Simpson's Rule is Exact for Cubics: A Simple Proof." Missouri J. Math. Sci. 17 (2) 100 - 105, Spring 2005. https://doi.org/10.35834/2005/1702100
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