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人気のある微分積分 >

integral from 0 to 4 of pi|4x-x^2|

解

\int_{0}^{4} π 4 x - x^{2} d x

解

π \frac{32}{3}

+1

十進法表記

33.51032 \dots

解答ステップ

\int_{0}^{4} π 4 x - x^{2} d x

絶対数を排除する

= \int_{0}^{4} π (4 x - x^{2}) d x

定数を除く:

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

= π \cdot \int_{0}^{4} 4 x - 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

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

\int_{0}^{4} 4 x d x = 32

\int_{0}^{4} x^{2} d x = \frac{64}{3}

= π (32 - \frac{64}{3})

結合

32 - \frac{64}{3} : \frac{32}{3}

= π \frac{32}{3}

グラフ

人気の例

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\int_{0}^{3} (5 x^{2} + 9 x) d x

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\int_{\frac{π}{6}}^{\frac{π}{3}} csc (x) d x