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NewtonCotesError[n, f, a, b]
gives the error in the elementary n-point Newton-Cotes quadrature formula for the function f on an interval from a to b.
  • The function f may be a pure function or a named function defined using Set or SetDelayed.
  • The error is given as a function of n, a and b multiplied by an mth derivative of the function f. The size of the error is bounded by the maximum of this expression over the interval from a to b.
  • The abscissas may or may not include the endpoints a and b of the interval. The option QuadratureType is used to control whether endpoints are included as abscissas.
  • With the default setting QuadratureType->Closed, the endpoints are included as abscissas.
  • With the setting QuadratureType->Open, the endpoints are not included as abscissas. In this case, the initial abscissa is chosen to be a halfstep above the lower endpoint.