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人気のある微分積分 >

integral from 2 to 6 of y/(sqrt(y-2))

解

\int_{2}^{6} \frac{y}{y - 2} d y

解

\frac{40}{3}

+1

十進法表記

13.33333 \dots

解答ステップ

\int_{2}^{6} \frac{y}{y - 2} d y

u置換積分法を適用する

= \int_{0}^{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_{0}^{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_{0}^{2} u^{2} d u + \int_{0}^{2} 2 d u)

\int_{0}^{2} u^{2} d u = \frac{8}{3}

\int_{0}^{2} 2 d u = 4

= 2 (\frac{8}{3} + 4)

簡素化

2 (\frac{8}{3} + 4) : \frac{40}{3}

= \frac{40}{3}

グラフ

人気の例

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\int_{1}^{2} (20 x^{3} + \frac{6}{x ^{2}}) d x

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\int_{0}^{10} (10 x - x^{2}) d x

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\int_{- 2}^{3} (2 x^{4} + 2 x^{3} - x + 7) d x

integral from 0 to 2pi of-100sin^2(t)

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