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Beliebt Rechnen >

integral from 0 to 3 of x/(sqrt(9-x^2))

Lösung

\int_{0}^{3} \frac{x}{9 - x ^{2}} d x

Lösung

3

Schritte zur Lösung

\int_{0}^{3} \frac{x}{9 - x ^{2}} d x

Wende U-Substitution an

= \int_{9}^{0} - \frac{1}{2 u} d u

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

= - \int_{0}^{9} - \frac{1}{2 u} d u

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{0}^{9} \frac{1}{u} d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [2 u^{\frac{1}{2}}]_{0}^{9})

Vereinfache

- (- \frac{1}{2} [2 u^{\frac{1}{2}}]_{0}^{9}) : \frac{1}{2} [2 u]_{0}^{9}

= \frac{1}{2} [2 u]_{0}^{9}

Berechne die Grenzen:

6

= \frac{1}{2} \cdot 6

Vereinfache

= 3

Graph

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