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Más información sobre la integración
E–5
f (x)
x
El gráfico es un pico muy próximo al origen. Dado que ningún punto de
muestra descubrió el pico, el algoritmo supone que f(x) era idéntico a cero en
todo el intervalo de integración. Aún cuando haya aumentado el número de
puntos de muestra mediante el cálculo de la integral en el formato SCI 11 o ALL,
ninguno de los puntos adicionales descubriría el pico cuando esta función en
concreto se integre en este intervalo particular. Para obtener soluciones a
problemas como éste, consulte el siguiente tema, "Condiciones que podrían
prolongar el tiempo de cálculo".
Por fortuna, las funciones que muestran tales aberraciones (una fluctuación que
no es característica de la función) son bastante poco usuales por lo que no es
probable que tenga que integrar una sin saberlo. Una función que puede
generar resultados incorrectos puede identificarse en términos sencillos
mediante la rapidez con la que ella y sus derivadas de orden bajo varían en el
intervalo de integración. Básicamente, cuanto más rápida sea la variación de la
función o sus derivadas y cuanto menor sea el orden de esas derivadas que
varían con rapidez, más lento será el cálculo y menos fiable será la
aproximación resultante.
365


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