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

解

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

\frac{128}{15}

十進法表記

8.53333 \dots

解答ステップ

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

簡素化

= \int_{- 2}^{2} - x^{4} + 4 x^{2} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- 2}^{2} x^{4} d x + \int_{- 2}^{2} 4 x^{2} d x

\int_{- 2}^{2} x^{4} d x = \frac{64}{5}

\int_{- 2}^{2} 4 x^{2} d x = \frac{64}{3}

= - \frac{64}{5} + \frac{64}{3}

簡素化

- \frac{64}{5} + \frac{64}{3} : \frac{128}{15}

= \frac{128}{15}