integral from 0 to 1 of (5x^e+7e^x)

解答

\int_{0}^{1} (5 x^{e} + 7 e^{x}) d x

\frac{5}{e + 1} + 7 (e - 1)

十进制

13.37267 \dots

求解步骤

\int_{0}^{1} 5 x^{e} + 7 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} 5 x^{e} d x + \int_{0}^{1} 7 e^{x} d x

\int_{0}^{1} 5 x^{e} d x = \frac{5}{e + 1}

\int_{0}^{1} 7 e^{x} d x = 7 (e - 1)

= \frac{5}{e + 1} + 7 (e - 1)

\int_{0}^{2} (3 x^{2} - x + 1) d x

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