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We consider families of general four-point quadratureformulae using a generalization of the Montgomery identity via Taylor’sformula. The results are applied to obtain some sharp inequalities for functionswhose derivatives belong to  spaces. Generalizations of Simpson’s3/8 formula and the Lobatto four-point formula with related inequalities areconsidered as special cases

Sharp Integral Inequalities Based on a General Four-Point Quadrature Formula via a Generalization of the Montgomery Identity