three-eighths rule

three-eighths rule

[¦thrē ′āths ‚rül]
(mathematics)
An approximation formula for definite integrals which states that the integral of a real-valued function ƒ on an interval [a, b ] is approximated by (3/8) h [ƒ(a) + 3ƒ(a + h) + 3ƒ(a + 2 h) + ƒ(b)], where h = (b-a)/3; this is the integral of a third-degree polynomial whose value equals that of ƒ at a, a + h, a + 2 h, and b.
A method of approximating a definite integral over an interval which is equivalent to dividing the interval into equal subintervals and applying the formula in the first definition to each subinterval.