Weddle's Rule

Let the values of a function  be tabulated at points  equally spaced by , so , , .... Then Weddle's rule approximating the integral of  is given by the Newton-Cotes-like formula

REFERENCES:

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 127, 1987.

King, A. E. "Approximate Integration. Note on Quadrature Formulae: Their Construction and Application to ActuHelvetica 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. The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, p. 151, 1967.