Centroidal Mean Derivative - Based Closed Newton Cotes Quadrature

In this paper, a new scheme of the evaluation of numerical integration by using Centroidal mean derivative - based closed Newton Cotes quadrature rule (CMDCNC) is presented in which the centroidal mean is used for the computation of function derivative. The accuracy of these numerical formulas are higher than the existing closed Newton Cotes quadrature (CNC) fromula. The error terms are also obtained by using the concept of precision. Comparisions are made between the existing closed Newton Cotes formula and the centroidal mean derivative - based closed Newton Cotes quadrature formula by using the numerical examples.