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

Lösung

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

\frac{40}{3}

Dezimale

13.33333 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} u^{2} + 2 d u

Wende die Summenregel an:

\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)

Vereinfache

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

= \frac{40}{3}

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