integral from-3 to 3 of (-5x^2-6x)^3

解答

\int_{- 3}^{3} (- 5 x^{2} - 6 x)^{3} d x

- \frac{914166}{7}

十进制

- 130595.14285 \dots

求解步骤

\int_{- 3}^{3} (- 5 x^{2} - 6 x)^{3} d x

乘开

(- 5 x^{2} - 6 x)^{3} : - 125 x^{6} - 450 x^{5} - 540 x^{4} - 216 x^{3}

= \int_{- 3}^{3} - 125 x^{6} - 450 x^{5} - 540 x^{4} - 216 x^{3} 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_{- 3}^{3} 125 x^{6} d x - \int_{- 3}^{3} 450 x^{5} d x - \int_{- 3}^{3} 540 x^{4} d x - \int_{- 3}^{3} 216 x^{3} d x

\int_{- 3}^{3} 125 x^{6} d x = \frac{546750}{7}

\int_{- 3}^{3} 450 x^{5} d x = 0

\int_{- 3}^{3} 540 x^{4} d x = 52488

\int_{- 3}^{3} 216 x^{3} d x = 0

= - \frac{546750}{7} - 0 - 52488 - 0

化简

- \frac{546750}{7} - 0 - 52488 - 0 : - \frac{914166}{7}

= - \frac{914166}{7}

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