integral from 1 to 8 of 6/t

Lösung

\int_{1}^{8} \frac{6}{t} d t

18 ln (2)

Dezimale

12.47664 \dots

Schritte zur Lösung

\int_{1}^{8} \frac{6}{t} d t

Entferne die Konstante:

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

= 6 \cdot \int_{1}^{8} \frac{1}{t} d t

Nutze das gemeinsame Integral :

\int \frac{1}{t} d t = ln (∣ t ∣)

= 6 [ln ∣ t ∣]_{1}^{8}

Berechne die Grenzen:

3 ln (2)

= 6 \cdot 3 ln (2)

Vereinfache

= 18 ln (2)

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