Boole's rule - Alchetron, The Free Social Encyclopedia

The widely propagated typographical error Bode's rule redirects here. For Bode's Law see Titius–Bode law.
In mathematics, Boole's rule, named after George Boole, is a method of numerical integration. It approximates an integral

∫ x 1 x 5 f ( x ) d x

by using the values of ƒ at five equally spaced points

x 1 , x 2 = x 1 + h , x 3 = x 1 + 2 h , x 4 = x 1 + 3 h , x 5 = x 1 + 4 h .

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

∫ x 1 x 5 f ( x ) d x = 2 h 45 ( 7 f ( x 1 ) + 32 f ( x 2 ) + 12 f ( x 3 ) + 32 f ( x 4 ) + 7 f ( x 5 ) ) + error term ,

and the error term is

− 8 945 h 7 f ( 6 ) ( c )

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).

References

Boole's rule Wikipedia

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