integral from 1/2 to 1 of 1/(2x)

Lösung

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

\frac{1}{2} ln (2)

Dezimale

0.34657 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{\frac{1}{2}}^{1} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{2} [ln ∣ x ∣]_{\frac{1}{2}}^{1}

Berechne die Grenzen:

ln (2)

= \frac{1}{2} ln (2)

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