Quadrature rules using an arbitrary fixed order of derivatives

In this paper we consider quadrature formulas which use the derivative of only an arbitrary fixed order (m) of function f at the nodes. One of the advantages of the new approach is that we can increase the precision degree of the n-point quadrature formulas from 2n-1 to 2n+m-1. Furthermore we give an asymptotic estimation for the rate of convergence of this formula. Some examples will be given to support the results.