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+ 2h) + ƒ(b)], whereh= (b-a)/3; this is the integral of a third-degree polynomial whose value equals that of ƒ ata,a+h,a+ 2h, andb.

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.