integral from-1 to 4 of x^2+x-2

解答

\int_{- 1}^{4} x^{2} + x - 2 d x

\frac{115}{6}

十进制

19.16666 \dots

求解步骤

\int_{- 1}^{4} x^{2} + x - 2 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_{- 1}^{4} x^{2} d x + \int_{- 1}^{4} x d x - \int_{- 1}^{4} 2 d x

\int_{- 1}^{4} x^{2} d x = \frac{65}{3}

\int_{- 1}^{4} x d x = \frac{15}{2}

\int_{- 1}^{4} 2 d x = 10

= \frac{65}{3} + \frac{15}{2} - 10

化简

\frac{65}{3} + \frac{15}{2} - 10 : \frac{115}{6}

= \frac{115}{6}

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