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Hardy's 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_7=f(x_7). Then Hardy's rule approximating the integral of f(x) is given by the Newton-Cotes-like formula

int_(x_1)^(x_7)f(x)dx=1/(100)h(28f_1+162f_2+220f_4+162f_6+28f_7).

See also

Boole's Rule, Durand's Rule, Newton-Cotes Formulas, Shovelton's Rule, Simpson's 3/8 Rule, Simpson's Rule, Trapezoidal Rule, Weddle's Rule

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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.

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Hardy's Rule

Cite this as:

Weisstein, Eric W. "Hardy's Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HardysRule.html

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