Newton-Cotes interpolation formula

One of the easiest ways to obtain useful quadrature formulas for our purpose is to use Lagrangian interpolation on an equally spaced mesh and integrate the result. This class of quadrature formulas is called the Newton-Cotes... 

The second way of employing the Newton-Cotes numerical integration formula is to consider it with quadratic interpolations or with three points approximation nevertheless, for that the interval [a,b] is now more grainy divided, namely in 2n equal sub-intervals ... 

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