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Simpson's 3/8 Rule

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_4=f(x_4). Then Simpson's 3/8 rule approximating the integral of f(x) is given by the Newton-Cotes-like formula

int_(x_1)^(x_4)f(x)dx=3/8h(f_1+3f_2+3f_3+f_4)-3/(80)h^5f^((4))(xi).

See also

Boole's Rule, Newton-Cotes Formulas, Simpson's Rule

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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.

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Simpson's 3/8 Rule

Cite this as:

Weisstein, Eric W. "Simpson's 3/8 Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Simpsons38Rule.html

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