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NewtonCotesWeights[n, a, b]
gives a list of the n pairs {xi, wi} of the elementary n-point Newton-Cotes formula for quadrature on the interval a to b, where wi is the weight of the abscissa xi.
  • 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.