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This Demonstration shows the Newton–Cotes quadrature formulas of integration and their application to the integration of

The Newton–Cotes integration formulas are just the integrals of interpolating polynomials.

The Newton–Cotes formulas may be "closed" if the endpoints

and

are used to obtain the interpolating polynomial.

The Newton–Cotes formulas are "open" if the extremes of the interval

are not used to obtain the interpolating polynomial.

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Newton-Cotes Quadrature Formulas