gives a list of the n pairs of the elementary n-point Newton–Cotes formula for quadrature on the interval a to b, where is the weight of the abscissa .
- To use NewtonCotesWeights, you first need to load the Numerical Differential Equation Analysis Package using Needs["NumericalDifferentialEquationAnalysis`"].
- Newton–Cotes quadrature approximates the value of an integral as a linear combination of values of the integrand evaluated at equally spaced points: .
- 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 half step above the lower endpoint.