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Spring 2005 Simpson's Rule is Exact for Cubics: A Simple Proof
Rohan J. Dalpatadu, Elizabeth E. Freeman
Missouri J. Math. Sci. 17(2): 100-105 (Spring 2005). DOI: 10.35834/2005/1702100


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.


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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.


Published: Spring 2005
First available in Project Euclid: 22 August 2019

zbMATH: 1079.41027
Digital Object Identifier: 10.35834/2005/1702100

Primary: 65D30

Rights: Copyright © 2005 Central Missouri State University, Department of Mathematics and Computer Science


Vol.17 • No. 2 • Spring 2005
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