integral from-4 to 4 of (x^2+x-6)

解答

\int_{- 4}^{4} (x^{2} + x - 6) d x

- \frac{16}{3}

十进制

- 5.33333 \dots

求解步骤

\int_{- 4}^{4} 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_{- 4}^{4} x^{2} d x + \int_{- 4}^{4} x d x - \int_{- 4}^{4} 6 d x

\int_{- 4}^{4} x^{2} d x = \frac{128}{3}

\int_{- 4}^{4} x d x = 0

\int_{- 4}^{4} 6 d x = 48

= \frac{128}{3} + 0 - 48

化简

\frac{128}{3} + 0 - 48 : - \frac{16}{3}

= - \frac{16}{3}

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