integral from 0 to pi/4 of cos^3(θ)

Lösung

\int_{0}^{\frac{π}{4}} cos^{3} (θ) d θ

\frac{5}{6 2}

Dezimale

0.58925 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} cos^{3} (θ) d θ

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{\frac{π}{4}} (1 - sin^{2} (θ)) cos (θ) d θ

Wende U-Substitution an

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

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

\int_{0}^{\frac{2}{2}} u^{2} d u = \frac{1}{6 2}

= \frac{1}{2} - \frac{1}{6 2}

Vereinfache

\frac{1}{2} - \frac{1}{6 2} : \frac{5}{6 2}

= \frac{5}{6 2}

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