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人気のある微分積分 >

integral from 0 to 1 of 2x(4-x^2)

解

\int_{0}^{1} 2 x (4 - x^{2}) d x

解

\frac{7}{2}

+1

十進法表記

3.5

解答ステップ

\int_{0}^{1} 2 x (4 - x^{2}) 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}^{1} x (4 - x^{2}) d x

拡張

x (4 - x^{2}) : 4 x - x^{3}

= 2 \cdot \int_{0}^{1} 4 x - x^{3} 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}^{1} 4 x d x - \int_{0}^{1} x^{3} d x)

\int_{0}^{1} 4 x d x = 2

\int_{0}^{1} x^{3} d x = \frac{1}{4}

= 2 (2 - \frac{1}{4})

簡素化

2 (2 - \frac{1}{4}) : \frac{7}{2}

= \frac{7}{2}

グラフ

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