integral from 1 to 8 of (10)/x

Lösung

\int_{1}^{8} \frac{10}{x} d x

30 ln (2)

Dezimale

20.79441 \dots

Schritte zur Lösung

\int_{1}^{8} \frac{10}{x} d x

Entferne die Konstante:

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

= 10 \cdot \int_{1}^{8} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 10 [ln ∣ x ∣]_{1}^{8}

Berechne die Grenzen:

3 ln (2)

= 10 \cdot 3 ln (2)

Vereinfache

= 30 ln (2)

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