Derivative based two-point gauss legendre rule for the riemann-stieltjes integral

Abstract

In this paper, derivative based two point Gauss-Legendre rule for the Riemann-Stieltjes integral is presented which uses derivative value in order to approximate the Riemann-Stieltjesintegral ∫1-1f(t) d g(t).This integral rule increases the order of the precision over the two point Gauss- Legendre rule meant for the Riemann-Stieltjes integration and the error term for the approximation is investigated.