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人気のある微分積分 >

integral from 0 to 2 of 7x(x-7)

解

\int_{0}^{2} 7 x (x - 7) d x

解

- \frac{238}{3}

+1

十進法表記

- 79.33333 \dots

解答ステップ

\int_{0}^{2} 7 x (x - 7) d x

定数を除く:

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

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

拡張

x (x - 7) : x^{2} - 7 x

= 7 \cdot \int_{0}^{2} x^{2} - 7 x 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

= 7 (\int_{0}^{2} x^{2} d x - \int_{0}^{2} 7 x d x)

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 7 x d x = 14

= 7 (\frac{8}{3} - 14)

簡素化

7 (\frac{8}{3} - 14) : - \frac{238}{3}

= - \frac{238}{3}

グラフ

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