Trapezoidal Rule

Trapezoidal Rule

The 2-point Newton-Cotes formula where , is the separation between the points, and is a point satisfying . Picking to maximize 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. [Pages Linking Here] 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. CITE THIS AS: Weisstein, Eric W. "Trapezoidal Rule." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/TrapezoidalRule.html