integral from-1 to 1 of (8x^2-1)^2

解

\int_{- 1}^{1} (8 x^{2} - 1)^{2} d x

\frac{254}{15}

十進法表記

16.93333 \dots

解答ステップ

\int_{- 1}^{1} (8 x^{2} - 1)^{2} d x

拡張

(8 x^{2} - 1)^{2} : 64 x^{4} - 16 x^{2} + 1

= \int_{- 1}^{1} 64 x^{4} - 16 x^{2} + 1 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_{- 1}^{1} 64 x^{4} d x - \int_{- 1}^{1} 16 x^{2} d x + \int_{- 1}^{1} 1 d x

\int_{- 1}^{1} 64 x^{4} d x = \frac{128}{5}

\int_{- 1}^{1} 16 x^{2} d x = \frac{32}{3}

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

= \frac{128}{5} - \frac{32}{3} + 2

簡素化

\frac{128}{5} - \frac{32}{3} + 2 : \frac{254}{15}

= \frac{254}{15}