2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73311We give an Euler-Maclaurin formula with remainder for the weighted sum of the values of a smooth function on the integral points in a simple integral polytope. Our work generalizes the formula obtained by Karshon, Sternberg and Weitsman in the ''Euler-Maclaurin with remainder for a simple integral polytope''.11 pages; to appear in the Asian Journal of MathematicsCombinatorics65B15; 52B20text