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人気のある微分積分 >

integral from 0 to 1 of 4x^3(4-x^4)

解

\int_{0}^{1} 4 x^{3} (4 - x^{4}) d x

解

\frac{7}{2}

+1

十進法表記

3.5

解答ステップ

\int_{0}^{1} 4 x^{3} (4 - x^{4}) d x

定数を除く:

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

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

拡張

x^{3} (4 - x^{4}) : 4 x^{3} - x^{7}

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

= 4 (\int_{0}^{1} 4 x^{3} d x - \int_{0}^{1} x^{7} d x)

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

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

= 4 (1 - \frac{1}{8})

簡素化

4 (1 - \frac{1}{8}) : \frac{7}{2}

= \frac{7}{2}

グラフ

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