integral from 0 to 2 of (3-x)(x-4)

解答

\int_{0}^{2} (3 - x) (x - 4) d x

- \frac{38}{3}

十进制

- 12.66666 \dots

求解步骤

\int_{0}^{2} (3 - x) (x - 4) d x

乘开

(3 - x) (x - 4) : 7 x - x^{2} - 12

= \int_{0}^{2} 7 x - x^{2} - 12 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}^{2} 7 x d x - \int_{0}^{2} x^{2} d x - \int_{0}^{2} 12 d x

\int_{0}^{2} 7 x d x = 14

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 12 d x = 24

= 14 - \frac{8}{3} - 24

化简

14 - \frac{8}{3} - 24 : - \frac{38}{3}

= - \frac{38}{3}

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