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Beliebt Rechnen >

integral from 0 to 5 of (x/(sqrt(x+4)))

Lösung

\int_{0}^{5} (\frac{x}{x + 4}) d x

Lösung

\frac{14}{3}

+1

Dezimale

4.66666 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{x}{x + 4} d x

Wende U-Substitution an

= \int_{2}^{3} 2 (u^{2} - 4) d u

Entferne die Konstante:

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

= 2 \cdot \int_{2}^{3} u^{2} - 4 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_{2}^{3} u^{2} d u - \int_{2}^{3} 4 d u)

\int_{2}^{3} u^{2} d u = \frac{19}{3}

\int_{2}^{3} 4 d u = 4

= 2 (\frac{19}{3} - 4)

Vereinfache

2 (\frac{19}{3} - 4) : \frac{14}{3}

= \frac{14}{3}

Graph

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