integral from 0 to 1 of (1+e^x)

解答

\int_{0}^{1} (1 + e^{x}) d x

e

十进制

2.71828 \dots

求解步骤

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

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

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

= 1 + e - 1

化简

= e

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