A Proposed Numerical Integration Method Using Polynomial Interpolation

The main aim of this paper is to propose a numerical integration method using polynomial interpolation that provides improved estimates as compared to the Newton-Cotes methods of integration. The method is an extension of trapezoidal rule where the Lagrange interpolation is employed when fitting polynomials after segmentation. We proved that the proposed numerical integration method using polynomial interpolation provided an improved formula for numerical integration. The proposed method using polynomial interpolation gave better estimates as compared to some Newton-Cotes methods of integration.