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人気のある微分積分 >

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

解

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

解

56

解答ステップ

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

拡張

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

= \int_{0}^{4} x^{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

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

\int_{0}^{4} x^{3} d x = 64

\int_{0}^{4} x d x = 8

= 64 - 8

簡素化

= 56

グラフ

人気の例

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\int_{0}^{4} \frac{1}{6 x + 1} d x

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\int_{2}^{6} x^{3} d x