Numerical integration using the derivatives

In this paper we establish the following formula to calculate the numerical computation of the integrals∫abw(x)f(x)dx≃∑i=1nwif(j)(xi);j=0,1,2,…,where f(j)(x) is the jth derivative of f(x). Calculating the nodes and xi weights wi with respect to the degree of accuracy are considered. Finally some numerical examples are given to compare the results with other well-known methods.