integral from-1 to 1 of-x^2+9

解答

\int_{- 1}^{1} - x^{2} + 9 d x

\frac{52}{3}

十进制

17.33333 \dots

求解步骤

\int_{- 1}^{1} - x^{2} + 9 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}^{1} x^{2} d x + \int_{- 1}^{1} 9 d x

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

\int_{- 1}^{1} 9 d x = 18

= - \frac{2}{3} + 18

化简

- \frac{2}{3} + 18 : \frac{52}{3}

= \frac{52}{3}

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