Let the values of a function 
be tabulated at points 
equally spaced by 
, so 
, 
, ..., 
. Then Shovelton's rule approximating the integral
of 
is given by the Newton-Cotes-like formula
![int_(x_1)^(x_(11))f(x)dx=5/(126)h[8(f_1+f_(11))+35(f_2+f_4+f_8+f_(10))
+15(f_3+f_5+f_7+f_9)+36f_6].](/images/equations/ShoveltonsRule/NumberedEquation1.svg) |
Shovelton's Rule
See also
Boole's Rule, Hardy's Rule, Newton-Cotes Formulas, Simpson's 3/8 Rule, Simpson's Rule, Trapezoidal Rule, Weddle's RuleExplore with Wolfram|Alpha
References
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. The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, p. 151, 1967.Referenced on Wolfram|Alpha
Shovelton's RuleCite this as:
Weisstein, Eric W. "Shovelton's Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ShoveltonsRule.html