integral from 3 to 6 of 2/(x-2)

Lösung

\int_{3}^{6} \frac{2}{x - 2} d x

4 ln (2)

Dezimale

2.77258 \dots

Schritte zur Lösung

\int_{3}^{6} \frac{2}{x - 2} d x

Entferne die Konstante:

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

= 2 \cdot \int_{3}^{6} \frac{1}{x - 2} d x

Wende U-Substitution an

= 2 \cdot \int_{1}^{4} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{1}^{4}

Berechne die Grenzen:

2 ln (2)

= 2 \cdot 2 ln (2)

Vereinfache

= 4 ln (2)

\int_{- 1}^{2} (2 x^{2} - x^{3}) d x

\int_{1}^{e^{2}} 2 π y ln (y) d y

\int_{0}^{5} 2 x^{3} - 3 x^{2} + 4 x + 1 d x

\int_{0}^{1.3} \frac{1}{6} x d x

\int_{- π}^{0} (x - π) sin (n x) d x