Definition

The degree of accuracy, or precision, of a quadrature formula is the positive integer [Maple Math] such that [Maple Math] for all polynomials [Maple Math] of degree less than or equal to [Maple Math] , but [Maple Math] , for some polynomial of degree [Maple Math] . Here [Maple Math] is the error term of the quadrature formula.

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Since integration and summation are both linear operations, the degree of accuracy can also be written with the conditions [Maple Math] for [Maple Math] and [Maple Math] .

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This means that the [Maple Math] point closed Newton-Cotes formulae with [Maple Math] even have a degree of precision equal to [Maple Math] . The [Maple Math] point Newton-Cotes formulae with [Maple Math] odd only have a degree of accuracy equal to [Maple Math] .

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