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人気のある微分積分 >

integral from 0 to 1 of 2pix(x^5-x^6)

解

\int_{0}^{1} 2 π x (x^{5} - x^{6}) d x

解

\frac{π}{28}

+1

十進法表記

0.11219 \dots

解答ステップ

\int_{0}^{1} 2 π x (x^{5} - x^{6}) d x

定数を除く:

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

= 2 π \cdot \int_{0}^{1} x (x^{5} - x^{6}) d x

拡張

x (x^{5} - x^{6}) : x^{6} - x^{7}

= 2 π \cdot \int_{0}^{1} x^{6} - x^{7} 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 π (\int_{0}^{1} x^{6} d x - \int_{0}^{1} x^{7} d x)

\int_{0}^{1} x^{6} d x = \frac{1}{7}

\int_{0}^{1} x^{7} d x = \frac{1}{8}

= 2 π (\frac{1}{7} - \frac{1}{8})

簡素化

2 π (\frac{1}{7} - \frac{1}{8}) : \frac{π}{28}

= \frac{π}{28}

グラフ

人気の例

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