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Sharp error bounds in approximating the Riemann-Stieltjes integral ∫abf(t)du(t)Open image in new window with the generalised trapezoid formula f(b)[u(b)−1b−a∫abu(s)ds]+f(a)[1b−a∫abu(s)ds−u(a)]Open image in new window are given for various pairs (f,u)Open image in new window of functions. Applications for weighted integrals are also provided.

Sharp error bounds in approximating the Riemann-Stieltjes integral by a generalised trapezoid formula and applications