integral from-pi/6 to pi/6 of 8sec^2(x)

Lösung

\int_{- \frac{π}{6}}^{\frac{π}{6}} 8 sec^{2} (x) d x

\frac{16}{3}

Dezimale

9.23760 \dots

Schritte zur Lösung

\int_{- \frac{π}{6}}^{\frac{π}{6}} 8 sec^{2} (x) d x

Entferne die Konstante:

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

= 8 \cdot \int_{- \frac{π}{6}}^{\frac{π}{6}} sec^{2} (x) d x

Nutze das gemeinsame Integral :

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

= 8 [tan (x)]_{- \frac{π}{6}}^{\frac{π}{6}}

Berechne die Grenzen:

\frac{2}{3}

= 8 \cdot \frac{2}{3}

Vereinfache

= \frac{16}{3}

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