integral from 0 to 2 of 1/(3x+1)

Lösung

\int_{0}^{2} \frac{1}{3 x + 1} d x

\frac{1}{3} ln (7)

Dezimale

0.64863 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{1}{3 x + 1} d x

Wende U-Substitution an

= \int_{1}^{7} \frac{1}{3 u} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{1}^{7} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{1}^{7}

Berechne die Grenzen:

ln (7)

= \frac{1}{3} ln (7)

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