On corrected Euler-Simpson's 3/8 formulae

Abstract

The aim of this paper is to derive corrected Euler-Simpson's 3/8 formulae, i.e. closed type quadrature formulae where the integral is approximated not only with the values of the function in points $a$, $(2a + b)/3$, $(a + 2b)/3$ and $b$, but also with values of the first derivative in boundary points of the interval. These formulae will have a higher degree of exactness than formulae obtained in [4]. Using the derived formulae, a number of inequalities for various classes of functions are obtained.