integral from-2 to 2 of (1-(x^2)/4)^2

解

\int_{- 2}^{2} (1 - \frac{x ^{2}}{4})^{2} d x

\frac{32}{15}

十進法表記

2.13333 \dots

解答ステップ

\int_{- 2}^{2} (1 - \frac{x ^{2}}{4})^{2} d x

拡張

(1 - \frac{x ^{2}}{4})^{2} : 1 - \frac{x ^{2}}{2} + \frac{x ^{4}}{16}

= \int_{- 2}^{2} 1 - \frac{x ^{2}}{2} + \frac{x ^{4}}{16} 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} 1 d x - \int_{- 2}^{2} \frac{x ^{2}}{2} d x + \int_{- 2}^{2} \frac{x ^{4}}{16} d x

\int_{- 2}^{2} 1 d x = 4

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

\int_{- 2}^{2} \frac{x ^{4}}{16} d x = \frac{4}{5}

= 4 - \frac{8}{3} + \frac{4}{5}

簡素化

4 - \frac{8}{3} + \frac{4}{5} : \frac{32}{15}

= \frac{32}{15}