integral from 0 to 1 of e-e^x

解答

\int_{0}^{1} e - e^{x} d x

1

求解步骤

\int_{0}^{1} e - e^{x} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} e d x - \int_{0}^{1} e^{x} d x

\int_{0}^{1} e d x = e

\int_{0}^{1} e^{x} d x = e - 1

= e - (e - 1)

化简

= 1

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