integral from 0 to pi/3 of 3sec(x)

Lösung

\int_{0}^{\frac{π}{3}} 3 sec (x) d x

3 ln (2 + 3)

Dezimale

3.95087 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{3}} 3 sec (x) d x

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

ln (2 + 3)

= 3 ln (2 + 3)

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