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人気のある微分積分 >

integral from 0 to 6 of x/(sqrt(25+4x))

解

\int_{0}^{6} \frac{x}{25 + 4 x} d x

解

\frac{17}{6}

+1

十進法表記

2.83333 \dots

解答ステップ

\int_{0}^{6} \frac{x}{25 + 4 x} d x

u置換積分法を適用する

= \int_{5}^{7} \frac{u ^{2} - 25}{8} d u

定数を除く:

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

= \frac{1}{8} \cdot \int_{5}^{7} u^{2} - 25 d u

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

= \frac{1}{8} (\int_{5}^{7} u^{2} d u - \int_{5}^{7} 25 d u)

\int_{5}^{7} u^{2} d u = \frac{218}{3}

\int_{5}^{7} 25 d u = 50

= \frac{1}{8} (\frac{218}{3} - 50)

簡素化

\frac{1}{8} (\frac{218}{3} - 50) : \frac{17}{6}

= \frac{17}{6}

グラフ

人気の例

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