Boole's Rule

Let the values of a function  be tabulated at points  equally spaced by , so , , ..., . Then Boole's rule approximating the integral of  is given by the Newton-Cotes-like formula

This formula is frequently and mistakenly known as Bode's rule (Abramowitz and Stegun 1972, p. 886) as a result of a typo in an early reference, but is actually due to Boole (Boole and Moulton 1960).

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.

Boole, G. and Moulton, J. F. A Treatise on the Calculus of Finite Differences, 2nd rev. ed. New York: Dover, 1960.