integral from 0 to pi/4 of 8sec^2(t)

Lösung

\int_{0}^{\frac{π}{4}} 8 sec^{2} (t) d t

8

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} 8 sec^{2} (t) d t

Entferne die Konstante:

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

= 8 \cdot \int_{0}^{\frac{π}{4}} sec^{2} (t) d t

Nutze das gemeinsame Integral :

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

= 8 [tan (t)]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

1

= 8 \cdot 1

Vereinfache

= 8

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