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Beliebt Rechnen >

integral from 1 to 9 of 1/(2x)

Lösung

\int_{1}^{9} \frac{1}{2 x} d x

Lösung

ln (3)

+1

Dezimale

1.09861 \dots

Schritte zur Lösung

\int_{1}^{9} \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_{1}^{9} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{2} [ln ∣ x ∣]_{1}^{9}

Berechne die Grenzen:

2 ln (3)

= \frac{1}{2} \cdot 2 ln (3)

Vereinfache

= ln (3)

Graph

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