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人気のある微分積分 >

integral from 3 to 6 of x/(sqrt(x-2))

解

\int_{3}^{6} \frac{x}{x - 2} d x

解

\frac{26}{3}

+1

十進法表記

8.66666 \dots

解答ステップ

\int_{3}^{6} \frac{x}{x - 2} d x

u置換積分法を適用する

= \int_{1}^{2} 2 (u^{2} + 2) d u

定数を除く:

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

= 2 \cdot \int_{1}^{2} u^{2} + 2 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

= 2 (\int_{1}^{2} u^{2} d u + \int_{1}^{2} 2 d u)

\int_{1}^{2} u^{2} d u = \frac{7}{3}

\int_{1}^{2} 2 d u = 2

= 2 (\frac{7}{3} + 2)

簡素化

2 (\frac{7}{3} + 2) : \frac{26}{3}

= \frac{26}{3}

グラフ

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