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Beliebt Rechnen >

integral from 0 to pi/6 of cos^3(x)

Lösung

\int_{0}^{\frac{π}{6}} cos^{3} (x) d x

Lösung

\frac{11}{24}

+1

Dezimale

0.45833 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{6}} cos^{3} (x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{\frac{π}{6}} (1 - sin^{2} (x)) cos (x) d x

Wende U-Substitution an

= \int_{0}^{\frac{1}{2}} 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

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

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

\int_{0}^{\frac{1}{2}} u^{2} d u = \frac{1}{24}

= \frac{1}{2} - \frac{1}{24}

Vereinfache

\frac{1}{2} - \frac{1}{24} : \frac{11}{24}

= \frac{11}{24}

Graph

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