integral from-3 to 3 of 1/2 (81-x^4)

解

\int_{- 3}^{3} \frac{1}{2} (81 - x^{4}) d x

\frac{972}{5}

十進法表記

194.4

解答ステップ

\int_{- 3}^{3} \frac{1}{2} (81 - x^{4}) d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- 3}^{3} 81 - 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

= \frac{1}{2} (\int_{- 3}^{3} 81 d x - \int_{- 3}^{3} x^{4} d x)

\int_{- 3}^{3} 81 d x = 486

\int_{- 3}^{3} x^{4} d x = \frac{486}{5}

= \frac{1}{2} (486 - \frac{486}{5})

簡素化

\frac{1}{2} (486 - \frac{486}{5}) : \frac{972}{5}

= \frac{972}{5}