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人気のある微分積分 >

integral from 0 to 3 of (x-1)^2

解

\int_{0}^{3} (x - 1)^{2} d x

解

3

解答ステップ

\int_{0}^{3} (x - 1)^{2} d x

拡張

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

= \int_{0}^{3} x^{2} - 2 x + 1 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}^{3} x^{2} d x - \int_{0}^{3} 2 x d x + \int_{0}^{3} 1 d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 2 x d x = 9

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

= 9 - 9 + 3

簡素化

= 3

グラフ

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