Woolhouse's formulas approximate a definite integral from equally spaced values of its integrand. Let the
values of a function be tabulated at points equally spaced by , so , , ..., . Then Woolhouse's formulas approximating the integral
of
are given by the Newton-Cotes-like formulas
King, A. E. "Approximate Integration. Note on Quadrature Formulae: Their Construction and Application to Actuarial Functions."
Trans. Faculty of Actuaries9, 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.
be tabulated at points 
equally spaced by 
, so 
, 
, ..., 
. Then Woolhouse's formulas approximating the integral
of 
are given by the Newton-Cotes-like formulas
![5[(223)/(3969)(f_1+f_(11))+(5875)/(18144)(f_2+f_(10))+(4625)/(10584)(f_4+f_8)+(41)/(112)f_5]](/images/equations/WoolhousesFormulas/Inline10.svg)
![14[7/(195)(f_1+f_(29))+(16807)/(66690)(f_3+f_(27))+(128)/(285)(f_8+f_(22))+(71)/(135)f_(15)].](/images/equations/WoolhousesFormulas/Inline13.svg)
