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Trapezoidal Rule

TrapezoidalRule

The 2-point Newton-Cotes formula

int_(x_1)^(x_2)f(x)dx=1/2h(f_1+f_2)-1/(12)h^3f^('')(xi),

where f_i=f(x_i), h is the separation between the points, and xi is a point satisfying x_1<=xi<=x_2. Picking xi to maximize f^('')(xi) gives an upper bound for the error in the trapezoidal approximation to the integral.

See also

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

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References

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 885, 1972.Whittaker, E. T. and Robinson, G. "The Trapezoidal and Parabolic Rules." The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 156-158, 1967.

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Trapezoidal Rule

Cite this as:

Weisstein, Eric W. "Trapezoidal Rule." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrapezoidalRule.html

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