Let the values of a function be tabulated at points equally spaced by , so , , ..., . Then Simpson's 3/8 rule approximating the integral of is given by the Newton-Cotes-like formula
Simpson's 3/8 Rule
See also
Boole's Rule, Newton-Cotes Formulas, Simpson's RuleExplore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 886, 1972.Jeffreys, H. and Jeffreys, B. S. Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 286-287, 1988.Whittaker, E. T. and Robinson, G. "The Trapezoidal and Parabolic Rules." The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 156-158, 1967.Referenced on Wolfram|Alpha
Simpson's 3/8 RuleCite this as:
Weisstein, Eric W. "Simpson's 3/8 Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Simpsons38Rule.html