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

Lösung

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

1

Schritte zur Lösung

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

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{2} [ln ∣ x ∣]_{1}^{e^{2}}

Berechne die Grenzen:

2

= \frac{1}{2} \cdot 2

Vereinfache

= 1

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