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

Lösung

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

4

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{4}^{0} - \frac{1}{u} d u

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

= - \int_{0}^{4} - \frac{1}{u} d u

Entferne die Konstante:

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

= - (- \int_{0}^{4} \frac{1}{u} d u)

Wende die Potenzregel an

= - (- [2 u^{\frac{1}{2}}]_{0}^{4})

Vereinfache

- (- [2 u^{\frac{1}{2}}]_{0}^{4}) : [2 u]_{0}^{4}

= [2 u]_{0}^{4}

Berechne die Grenzen:

4

= 4

\int_{- 1}^{3} 3 x^{2} + 5 x - 1 d x

\int_{4}^{5} 5 d x

\int_{0}^{1} 3 x^{2} sin (x^{3}) d x

\int_{0}^{1} x \cdot e^{3 x} d x

\int_{1}^{2} x^{3} e^{x} d x