integral from 3 to 7 of (e^x-3x)

解答

\int_{3}^{7} (e^{x} - 3 x) d x

e^{7} - e^{3} - 60

十进制表示法

1016.54762 \dots

求解步骤

\int_{3}^{7} e^{x} - 3 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_{3}^{7} e^{x} d x - \int_{3}^{7} 3 x d x

\int_{3}^{7} e^{x} d x = e^{7} - e^{3}

\int_{3}^{7} 3 x d x = 60

= e^{7} - e^{3} - 60

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