integral from 0 to pi/2 of cos^2(θ)

Lösung

\int_{0}^{\frac{π}{2}} cos^{2} (θ) d θ

\frac{π}{4}

Dezimale

0.78539 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} cos^{2} (θ) d θ

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π}{2}} 1 + cos (2 θ) d θ

Wende die Summenregel an:

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

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

\int_{0}^{\frac{π}{2}} 1 d θ = \frac{π}{2}

\int_{0}^{\frac{π}{2}} cos (2 θ) d θ = 0

= \frac{1}{2} (\frac{π}{2} + 0)

Vereinfache

\frac{1}{2} (\frac{π}{2} + 0) : \frac{π}{4}

= \frac{π}{4}

\int_{0}^{\frac{π}{4}} tan^{2} (θ) d θ

\int_{0}^{e - 1} ln (x + 1) d x

\int_{0}^{1} \frac{x}{1 + x} d x

\int_{0}^{2} x^{2} - 1 d x

\int_{\frac{π}{6}}^{\frac{π}{2}} cos^{2} (u) d u