integral from-1 to 4 of 1/(sqrt(4-x))

Lösung

\int_{- 1}^{4} \frac{1}{4 - x} d x

25

Dezimale

4.47213 \dots

Schritte zur Lösung

\int_{- 1}^{4} \frac{1}{4 - x} d x

Wende U-Substitution an

= \int_{5}^{0} - \frac{1}{u} d u

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

= - \int_{0}^{5} - \frac{1}{u} d u

Entferne die Konstante:

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

= - (- \int_{0}^{5} \frac{1}{u} d u)

Wende die Potenzregel an

= - (- [2 u^{\frac{1}{2}}]_{0}^{5})

Vereinfache

- (- [2 u^{\frac{1}{2}}]_{0}^{5}) : [2 u]_{0}^{5}

= [2 u]_{0}^{5}

Berechne die Grenzen:

25

= 25

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