integral from 0 to pi/4 of (5sec^2(x))

Lösung

\int_{0}^{\frac{π}{4}} (5 sec^{2} (x)) d x

5

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} 5 sec^{2} (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}} sec^{2} (x) d x

Nutze das gemeinsame Integral :

\int sec^{2} (x) d x = tan (x)

= 5 [tan (x)]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

1

= 5 \cdot 1

Vereinfache

= 5

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