integral from-1 to 0 of 1/(1-x)

Lösung

\int_{- 1}^{0} \frac{1}{1 - x} d x

ln (2)

Dezimale

0.69314 \dots

Schritte zur Lösung

\int_{- 1}^{0} \frac{1}{1 - x} d x

Wende U-Substitution an

= \int_{2}^{1} - \frac{1}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{2} - \frac{1}{u} d u

Entferne die Konstante:

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

= - (- \int_{1}^{2} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- [ln ∣ u ∣]_{1}^{2})

Vereinfache

= [ln ∣ u ∣]_{1}^{2}

Berechne die Grenzen:

ln (2)

= ln (2)

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