integral from 0 to 1 of e^{-x}-e^x

解答

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

2 - e - \frac{1}{e}

十进制

- 1.08616 \dots

求解步骤

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

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

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

= 1 - \frac{1}{e} - (e - 1)

化简

= 2 - e - \frac{1}{e}

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