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人気のある微分積分 >

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

解

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

解

\frac{16}{3}

+1

十進法表記

5.33333 \dots

解答ステップ

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

簡素化

(2 1 - x^{2})^{2} : 4 (1 - x^{2})

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

定数を除く:

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

= 4 \cdot \int_{- 1}^{1} 1 - x^{2} 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_{- 1}^{1} 1 d x - \int_{- 1}^{1} x^{2} d x)

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

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

= 4 (2 - \frac{2}{3})

簡素化

4 (2 - \frac{2}{3}) : \frac{16}{3}

= \frac{16}{3}

グラフ

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