integral from 1 to e^8 of 4/x

Lösung

\int_{1}^{e^{8}} \frac{4}{x} d x

32

Schritte zur Lösung

\int_{1}^{e^{8}} \frac{4}{x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{e^{8}} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 4 [ln ∣ x ∣]_{1}^{e^{8}}

Berechne die Grenzen:

8

= 4 \cdot 8

Vereinfache

= 32

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