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Beliebt Rechnen >

integral from-40 to 0 of 1/(sqrt(9-x))

Lösung

\int_{- 40}^{0} \frac{1}{9 - x} d x

Lösung

8

Schritte zur Lösung

\int_{- 40}^{0} \frac{1}{9 - x} d x

Wende U-Substitution an

= \int_{49}^{9} - \frac{1}{u} d u

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

= - \int_{9}^{49} - \frac{1}{u} d u

Entferne die Konstante:

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

= - (- \int_{9}^{49} \frac{1}{u} d u)

Wende die Potenzregel an

= - (- [2 u^{\frac{1}{2}}]_{9}^{49})

Vereinfache

- (- [2 u^{\frac{1}{2}}]_{9}^{49}) : [2 u]_{9}^{49}

= [2 u]_{9}^{49}

Berechne die Grenzen:

8

= 8

Graph

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