integral from 0 to 2 of-x^4+2x^2+8

解答

\int_{0}^{2} - x^{4} + 2 x^{2} + 8 d x

\frac{224}{15}

十进制

14.93333 \dots

求解步骤

\int_{0}^{2} - x^{4} + 2 x^{2} + 8 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_{0}^{2} x^{4} d x + \int_{0}^{2} 2 x^{2} d x + \int_{0}^{2} 8 d x

\int_{0}^{2} x^{4} d x = \frac{32}{5}

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} 8 d x = 16

= - \frac{32}{5} + \frac{16}{3} + 16

化简

- \frac{32}{5} + \frac{16}{3} + 16 : \frac{224}{15}

= \frac{224}{15}

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