integral from 0 to pi/4 of 5/(cos(x))

Lösung

\int_{0}^{\frac{π}{4}} \frac{5}{cos ( x )} d x

5 ln (1 + 2)

Dezimale

4.40686 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} \frac{5}{cos ( x )} d x

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{\frac{π}{4}} \frac{1}{cos ( x )} d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 5 \cdot \int_{0}^{\frac{π}{4}} sec (x) d x

Nutze das gemeinsame Integral :

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

= 5 [ln ∣ tan (x) + sec (x) ∣]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

ln (1 + 2)

= 5 ln (1 + 2)

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