Forming a Mixed Quadrature Rule Using an Anti-Gaussian Quadrature Rule

Abstract

A mixed quadrature rule of higher precision for approximate evaluation of real definite integrals has been constructed using an anti-Gaussian rule. The analytical convergence of the rule has been studied. The relative efficiency of  the  mixed quadrature rule has been shown with the help of suitable test integrals. The error bounds have been determined asymptotically.