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E–8 Más información sobre la integración
|
X
!!
³ /
8

Integral. (El cálculo tarda uno o
dos minutos.)
[
8
.
Incertidumbre de aproximación.
Se trata de la respuesta correcta, pero tardó mucho en generarse. Para
entender el motivo, compare el gráfico de la función entre x = 0 y x = 10
3
,
cuyo aspecto es similar al mostrado en el ejemplo anterior, con el gráfico de la
función entre x = 0 y x = 10:
x
f (x)
0 10
Puede ver que esta función sólo es "interesante" con valores bajos de x. Si los
valores de x son altos, la función no es interesante dado que disminuye ligera y
gradualmente de un modo predecible.
El algoritmo realiza una muestra de la función con densidades más altas de los
puntos de muestra hasta que la disparidad entre las aproximaciones sucesivas
se hace suficientemente pequeña. Para un intervalo estrecho de un área en la
que la función es interesante, tarda menos tiempo en llegar a la densidad
crítica.
Para conseguir la misma densidad de los puntos de muestra, el número total de
puntos de muestra requerido para un intervalo más grande es mucho mayor que
el número requerido para un intervalo más pequeño. En consecuencia, se
requieren varias iteraciones más para que el intervalo más grande consiga una
aproximación con la misma precisión y, por tanto, el cálculo de la integral
requiere bastante más tiempo.
368


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