integral from 0 to 1 of (2e^{x/(3+4)}+5)

解答

\int_{0}^{1} (2 e^{\frac{x}{3 + 4}} + 5) d x

14 7 e - 9

十进制

7.14990 \dots

求解步骤

\int_{0}^{1} 2 e^{\frac{x}{3 + 4}} + 5 d x

化简

= \int_{0}^{1} 2 e^{\frac{x}{7}} + 5 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} 2 e^{\frac{x}{7}} d x + \int_{0}^{1} 5 d x

\int_{0}^{1} 2 e^{\frac{x}{7}} d x = 14 (7 e - 1)

\int_{0}^{1} 5 d x = 5

= 14 (7 e - 1) + 5

化简

14 (7 e - 1) + 5 : 14 7 e - 9

= 14 7 e - 9

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