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)(m) of function ff at the nodes. One of the advantages of the new approach is that we can increase the precision degree of the nn-point quadrature formulas from 2n−12n−1 to 2n+m−12n+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.