de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to pi/2 of (cos^2(x))

Lösung

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

Lösung

\frac{π}{4}

+1

Dezimale

0.78539 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

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 x) d x

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

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

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

= \frac{1}{2} (\frac{π}{2} + 0)

Vereinfache

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

= \frac{π}{4}

Graph

Beliebte Beispiele

tangent 2x^2+8x+9

t an g e n t 2 x^{2} + 8 x + 9

limit as x approaches 2+of (x-1)/(x-2)

x \to 2 + lim (\frac{x - 1}{x - 2})

integral from 1 to t of 15x^{-3}

\int_{1}^{t} 15 x^{- 3} d x

integral of sec(pix)tan(pix)

\int sec (π x) tan (π x) d x

integral of 8e^{8x-3}

\int 8 e^{8 x - 3} d x