integral from 1 to 10 of (5/x)

Lösung

\int_{1}^{10} (\frac{5}{x}) d x

5 ln (10)

Dezimale

11.51292 \dots

Schritte zur Lösung

\int_{1}^{10} \frac{5}{x} d x

Entferne die Konstante:

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

= 5 \cdot \int_{1}^{10} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{1}^{10}

Berechne die Grenzen:

ln (10)

= 5 ln (10)

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