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

解答

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

\frac{50}{3}

十进制

16.66666 \dots

求解步骤

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

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

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

\int_{- 1}^{4} 4 d x = 20

= \frac{65}{3} + 15 - 20

化简

\frac{65}{3} + 15 - 20 : \frac{50}{3}

= \frac{50}{3}

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