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人気のある微分積分 >

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

解

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

解

\frac{π}{4} - \frac{1}{2}

+1

十進法表記

0.28539 \dots

解答ステップ

\int_{0}^{1} 2 x - x^{2} - 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}^{1} 2 x - x^{2} d x - \int_{0}^{1} x d x

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

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

= \frac{π}{4} - \frac{1}{2}

グラフ

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