integral from 2 to 7 of x^2-2x-8

解答

\int_{2}^{7} x^{2} - 2 x - 8 d x

\frac{80}{3}

十进制

26.66666 \dots

求解步骤

\int_{2}^{7} x^{2} - 2 x - 8 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_{2}^{7} x^{2} d x - \int_{2}^{7} 2 x d x - \int_{2}^{7} 8 d x

\int_{2}^{7} x^{2} d x = \frac{335}{3}

\int_{2}^{7} 2 x d x = 45

\int_{2}^{7} 8 d x = 40

= \frac{335}{3} - 45 - 40

化简

\frac{335}{3} - 45 - 40 : \frac{80}{3}

= \frac{80}{3}

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