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

Lösung

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

\frac{4}{3}

Dezimale

2.30940 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \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)

= 2 [tan (x)]_{- \frac{π}{6}}^{\frac{π}{6}}

Berechne die Grenzen:

\frac{2}{3}

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

Vereinfache

= \frac{4}{3}

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