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.

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.