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Beliebt Rechnen >

integral from 0 to pi/6 of 20sec^4(x)

Lösung

\int_{0}^{\frac{π}{6}} 20 sec^{4} (x) d x

Lösung

\frac{200}{9 3}

+1

Dezimale

12.83000 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{6}} 20 sec^{4} (x) d x

Entferne die Konstante:

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

= 20 \cdot \int_{0}^{\frac{π}{6}} sec^{4} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 20 \cdot \int_{0}^{\frac{π}{6}} (1 + tan^{2} (x)) sec^{2} (x) d x

Wende U-Substitution an

= 20 \cdot \int_{0}^{\frac{3}{3}} 1 + u^{2} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 20 (\int_{0}^{\frac{3}{3}} 1 d u + \int_{0}^{\frac{3}{3}} u^{2} d u)

\int_{0}^{\frac{3}{3}} 1 d u = \frac{1}{3}

\int_{0}^{\frac{3}{3}} u^{2} d u = \frac{1}{9 3}

= 20 (\frac{1}{3} + \frac{1}{9 3})

Vereinfache

20 (\frac{1}{3} + \frac{1}{9 3}) : \frac{200}{9 3}

= \frac{200}{9 3}

Graph

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