integral from 2 to 4 of 2/(sqrt(x^2-4))

Lösung

\int_{2}^{4} \frac{2}{x ^{2} - 4} d x

2 ln (2 + 3)

Dezimale

2.63391 \dots

Schritte zur Lösung

\int_{2}^{4} \frac{2}{x ^{2} - 4} d x

Entferne die Konstante:

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

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

Trigonometrische Substitution anwenden

= 2 \cdot \int_{0}^{\frac{π}{3}} sec (u) d u

Nutze das gemeinsame Integral :

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= 2 [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}}

Berechne die Grenzen:

ln (2 + 3)

= 2 ln (2 + 3)

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