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The Midpoint Method of Numerical Integration

Preston C. Hammer

Abstract

It is a noteworthy fact that while virtually all calculus texts and numerical analysis books discuss the trapezoidal method of numerical integration they ignore one which is simpler to use and generally superior to the trapezoidal-namely the midpoint rectangular method. The midpoint method also may be used with the trapezoidal method to obtain bounds for an integral in some cases. The midpoint method is an application of the Newton-Cotes open formulas with one point. The trapezoidal and midpoint methods over one interval of length h are given respectively in the following equations:

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Key concepts: Midpoint, Midpoint method, Trapezoidal rule, Mathematics, Interval (graph theory), Numerical integration, Point (geometry), Numerical analysis