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

解答

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

\frac{32}{3}

十进制

10.66666 \dots

求解步骤

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

使用分布积分法

= [\frac{1}{3} x^{3} (x + 2) - \int \frac{x ^{3}}{3} d x]_{- 2}^{2}

\int \frac{x ^{3}}{3} d x = \frac{x ^{4}}{12}

= [\frac{1}{3} x^{3} (x + 2) - \frac{x ^{4}}{12}]_{- 2}^{2}

化简

[\frac{1}{3} x^{3} (x + 2) - \frac{x ^{4}}{12}]_{- 2}^{2} : [\frac{1}{12} (3 x^{4} + 8 x^{3})]_{- 2}^{2}

= [\frac{1}{12} (3 x^{4} + 8 x^{3})]_{- 2}^{2}

带入上下限计算后得:

\frac{32}{3}

= \frac{32}{3}

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