integral from n to 2n of 1/x

Lösung

\int_{n}^{2 n} \frac{1}{x} d x

ln (2)

Dezimale

0.69314 \dots

Schritte zur Lösung

\int_{n}^{2 n} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{n}^{2 n}

Berechne die Grenzen:

ln (2 ∣ n ∣) - ln ∣ n ∣

= ln (2 ∣ n ∣) - ln ∣ n ∣

Vereinfache

= ln (2)

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