integral from-2 to 3 of (9-x^2)-(3-x)

解答

\int_{- 2}^{3} (9 - x^{2}) - (3 - x) d x

\frac{125}{6}

十进制

20.83333 \dots

求解步骤

\int_{- 2}^{3} 9 - x^{2} - (3 - x) d x

化简

= \int_{- 2}^{3} - x^{2} + x + 6 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}^{3} x^{2} d x + \int_{- 2}^{3} x d x + \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

\int_{- 2}^{3} x d x = \frac{5}{2}

\int_{- 2}^{3} 6 d x = 30

= - \frac{35}{3} + \frac{5}{2} + 30

化简

- \frac{35}{3} + \frac{5}{2} + 30 : \frac{125}{6}

= \frac{125}{6}

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