integral from-2 to 2 of 16-8x^2+x^4

解

\int_{- 2}^{2} 16 - 8 x^{2} + x^{4} d x

\frac{512}{15}

十進法表記

34.13333 \dots

解答ステップ

\int_{- 2}^{2} 16 - 8 x^{2} + x^{4} 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} 16 d x - \int_{- 2}^{2} 8 x^{2} d x + \int_{- 2}^{2} x^{4} d x

\int_{- 2}^{2} 16 d x = 64

\int_{- 2}^{2} 8 x^{2} d x = \frac{128}{3}

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

= 64 - \frac{128}{3} + \frac{64}{5}

簡素化

64 - \frac{128}{3} + \frac{64}{5} : \frac{512}{15}

= \frac{512}{15}