Boole's rule

In mathematics, Boole's rule, named after George Boole, is a method of numerical integration. It approximates an integral

by using the values of ƒ at five equally spaced points

It is expressed thus in Abramowitz and Stegun (1972, p. 886):

and the error term is

for some number c between x1 and x5. (945 = 1 × 3 × 5 × 7 × 9.)

It is often known as Bode's rule, due to a typographical error that propagated from Abramowitz and Stegun (1972, p. 886).[1][2]

See also


  1. Weisstein, Eric W. "Boole's Rule". MathWorld.
  2. Zucker, Ruth (1983) [June 1964]. "Chapter 25.4.14: Numerical Interpolation, Differentiation, and Integration - Integration - Numerical Analysis". In Abramowitz, Milton; Stegun, Irene Ann (eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 886. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.

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