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人気のある微分積分 >

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

解

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

解

\frac{136}{3}

+1

十進法表記

45.33333 \dots

解答ステップ

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

定数を除く:

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

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

拡張

x^{2} (x - 1) : x^{3} - x^{2}

= 4 \cdot \int_{1}^{3} x^{3} - x^{2} 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

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

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} x^{2} d x = \frac{26}{3}

= 4 (20 - \frac{26}{3})

簡素化

4 (20 - \frac{26}{3}) : \frac{136}{3}

= \frac{136}{3}

グラフ

人気の例

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