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人気のある微分積分 >

integral from 0 to 2 of 2pix(1+(x^2)/4)

解

\int_{0}^{2} 2 π x (1 + \frac{x ^{2}}{4}) d x

解

6 π

+1

十進法表記

18.84955 \dots

解答ステップ

\int_{0}^{2} 2 π x (1 + \frac{x ^{2}}{4}) d x

定数を除く:

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

= 2 π \cdot \int_{0}^{2} x (1 + \frac{x ^{2}}{4}) d x

拡張

x (1 + \frac{x ^{2}}{4}) : x + \frac{x ^{3}}{4}

= 2 π \cdot \int_{0}^{2} x + \frac{x ^{3}}{4} 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

= 2 π (\int_{0}^{2} x d x + \int_{0}^{2} \frac{x ^{3}}{4} d x)

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

\int_{0}^{2} \frac{x ^{3}}{4} d x = 1

= 2 π (2 + 1)

簡素化

= 6 π

グラフ

人気の例

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