integral from-pi/3 to pi/3 of 6sec^2(x)

Lösung

\int_{- \frac{π}{3}}^{\frac{π}{3}} 6 sec^{2} (x) d x

123

Dezimale

20.78460 \dots

Schritte zur Lösung

\int_{- \frac{π}{3}}^{\frac{π}{3}} 6 sec^{2} (x) d x

Entferne die Konstante:

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

= 6 \cdot \int_{- \frac{π}{3}}^{\frac{π}{3}} sec^{2} (x) d x

Nutze das gemeinsame Integral :

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

= 6 [tan (x)]_{- \frac{π}{3}}^{\frac{π}{3}}

Berechne die Grenzen:

23

= 6 \cdot 23

Vereinfache

= 123

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