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Durand'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_n=f(x_n). Then Durand's rule approximating the integral of f(x) is given by the Newton-Cotes-like formula

int_(x_1)^(x_n)f(x)dx=h(2/5f_1+(11)/(10)f_2+f_3+...+f_(n-2)+(11)/(10)f_(n-1)+2/5f_n).

See also

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

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References

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

Referenced on Wolfram|Alpha

Durand's Rule

Cite this as:

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

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