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.
Trapezoidal Rule
See also
Boole's Rule, Hardy's Rule, Newton-Cotes Formulas, Simpson's 3/8 Rule, Simpson's Rule, Weddle's RuleExplore with Wolfram|Alpha
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. https://mathworld.wolfram.com/TrapezoidalRule.html