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Newton-Cotes formulas

Newton-Cotes formulas are based on n + 1 equally spaced sample points a = x0 < x1 < x2 < ··· < xn = b. They take the formMATHwhere the weights wi are chosen so that their sum is 1 and so that the approximationMATHis exact for a polynomials of degree at most n.

Newton-Cotes formulas for $n=2,3,4,5$

MATH (Simpson's rule)MATH

MATH (Simpson's 3/8 rule)MATH

MATH MATH

MATHMATH


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


Gaussian quadrature

Simpson's rule

Trapezoidal rule


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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