integral from 0 to pi/4 of cos^3(x)

Lösung

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

\frac{5}{6 2}

Dezimale

0.58925 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

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}

\int_{0}^{2} 3^{x} (1 - 2^{x}) d x

\int_{- 6}^{6} ∣ x ∣ d x

\int_{1}^{6} ∣ 2 x - 4 ∣ d x

\int_{1}^{e} \frac{2 - ln ( x )}{x} d x

\int_{1}^{\infty} arctan (x) d x