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人気のある微分積分 >

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

解

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

解

8

解答ステップ

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

拡張

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

= \int_{- 1}^{3} x^{3} - 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_{- 1}^{3} x^{3} d x - \int_{- 1}^{3} 3 x d x

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

\int_{- 1}^{3} 3 x d x = 12

= 20 - 12

簡素化

= 8

グラフ

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