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人気のある微分積分 >

integral from 0 to 4 of 2pix(8-x^{3/2})

解

\int_{0}^{4} 2 π x (8 - x^{\frac{3}{2}}) d x

解

\frac{384 π}{7}

+1

十進法表記

172.33879 \dots

解答ステップ

\int_{0}^{4} 2 π x (8 - x^{\frac{3}{2}}) 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}^{4} x (8 - x^{\frac{3}{2}}) d x

拡張

x (8 - x^{\frac{3}{2}}) : 8 x - x^{\frac{5}{2}}

= 2 π \cdot \int_{0}^{4} 8 x - x^{\frac{5}{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

= 2 π (\int_{0}^{4} 8 x d x - \int_{0}^{4} x^{\frac{5}{2}} d x)

\int_{0}^{4} 8 x d x = 64

\int_{0}^{4} x^{\frac{5}{2}} d x = \frac{256}{7}

= 2 π (64 - \frac{256}{7})

簡素化

2 π (64 - \frac{256}{7}) : \frac{384 π}{7}

= \frac{384 π}{7}

グラフ

人気の例

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\int_{2}^{3} \frac{33}{3 - x} d x

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limit as x approaches infinity of 1/0

x \to \infty lim (\frac{1}{0})

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\int \frac{x ^{2}}{100 - x ^{2}} d x