gives a list of the n pairs {xi,wi} of the elementary n-point NewtonCotes formula for quadrature on the interval a to b, where wi is the weight of the abscissa xi.

Details and Options

  • To use NewtonCotesWeights, you first need to load the Numerical Differential Equation Analysis Package using Needs["NumericalDifferentialEquationAnalysis`"].
  • NewtonCotes 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.