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Beliebt Rechnen >

integral from 1 to 5 of x/(sqrt(5-x))

Lösung

\int_{1}^{5} \frac{x}{5 - x} d x

Lösung

\frac{44}{3}

+1

Dezimale

14.66666 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{x}{5 - x} d x

Wende U-Substitution an

= \int_{2}^{0} - 2 (- u^{2} + 5) d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{2} - 2 (- u^{2} + 5) 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} + 5 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} 5 d u))

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

\int_{0}^{2} 5 d u = 10

= - (- 2 (- \frac{8}{3} + 10))

Vereinfache

- (- 2 (- \frac{8}{3} + 10)) : \frac{44}{3}

= \frac{44}{3}

Graph

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