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人気のある微分積分 >

integral from 0 to 2 of-2x(2+x^5)

解

\int_{0}^{2} - 2 x (2 + x^{5}) d x

解

- \frac{312}{7}

+1

十進法表記

- 44.57142 \dots

解答ステップ

\int_{0}^{2} - 2 x (2 + x^{5}) d x

定数を除く:

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

= - 2 \cdot \int_{0}^{2} x (2 + x^{5}) d x

拡張

x (2 + x^{5}) : 2 x + x^{6}

= - 2 \cdot \int_{0}^{2} 2 x + x^{6} 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

= - 2 (\int_{0}^{2} 2 x d x + \int_{0}^{2} x^{6} d x)

\int_{0}^{2} 2 x d x = 4

\int_{0}^{2} x^{6} d x = \frac{128}{7}

= - 2 (4 + \frac{128}{7})

簡素化

- 2 (4 + \frac{128}{7}) : - \frac{312}{7}

= - \frac{312}{7}

グラフ

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