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人気のある微分積分 >

integral from 0 to 3 of 5x(x-3)

解

\int_{0}^{3} 5 x (x - 3) d x

解

- \frac{45}{2}

+1

十進法表記

- 22.5

解答ステップ

\int_{0}^{3} 5 x (x - 3) d x

定数を除く:

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

= 5 \cdot \int_{0}^{3} x (x - 3) d x

拡張

x (x - 3) : x^{2} - 3 x

= 5 \cdot \int_{0}^{3} x^{2} - 3 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

= 5 (\int_{0}^{3} x^{2} d x - \int_{0}^{3} 3 x d x)

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 3 x d x = \frac{27}{2}

= 5 (9 - \frac{27}{2})

簡素化

5 (9 - \frac{27}{2}) : - \frac{45}{2}

= - \frac{45}{2}

グラフ

人気の例

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\int_{0}^{\frac{x}{2}} sin (x) d x

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