Woolhouse's Formulas

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_n=f(x_n). Then Woolhouse's formulas approximating the integral of f(x) are given by the Newton-Cotes-like formulas


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King, A. E. "Approximate Integration. Note on Quadrature Formulae: Their Construction and Application to Actuarial Functions." Trans. Faculty of Actuaries 9, 218-231, 1923.Sheppard, W. F. "Some Quadrature-Formulæ." Proc. London Math. Soc. 32, 258-277, 1900.Whittaker, E. T. and Robinson, G. "Woolhouse's Formulae." The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, p. 158, 1967.Woolhouse, W. S. B. "On Integration by Means of Selected Values of the Function." J. Inst. Act. 27, 122-155, 1888.

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Woolhouse's Formulas

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Weisstein, Eric W. "Woolhouse's Formulas." From MathWorld--A Wolfram Web Resource.

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