integral from 0 to 2 of 4/(5x+1)

Lösung

\int_{0}^{2} \frac{4}{5 x + 1} d x

\frac{4}{5} ln (11)

Dezimale

1.91831 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{4}{5 x + 1} d x

Entferne die Konstante:

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

= 4 \cdot \int_{0}^{2} \frac{1}{5 x + 1} d x

Wende U-Substitution an

= 4 \cdot \int_{1}^{11} \frac{1}{5 u} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{5} \cdot \int_{1}^{11} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 \cdot \frac{1}{5} [ln ∣ u ∣]_{1}^{11}

Vereinfache

4 \cdot \frac{1}{5} [ln ∣ u ∣]_{1}^{11} : \frac{4}{5} [ln ∣ u ∣]_{1}^{11}

= \frac{4}{5} [ln ∣ u ∣]_{1}^{11}

Berechne die Grenzen:

ln (11)

= \frac{4}{5} ln (11)

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