A zero property for integrals

• Autores: Raghib M. Abu-Saris
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 40, Nº. 2, 2009, págs. 269-271
• Idioma: inglés
• DOI: 10.1080/00207390801935905
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• Resumen

  • In this note, we show that if the integral of a continuous function, h, vanishes over an interval [a, b], then so does the integral of w(x)h(x) over [a, c] for some c in (a, b), where w is a monotonic increasing (decreasing) function on [a, b] with w(a) is non-negative (non-positive).