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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{π}{4}

+1

Dezimale

0.78539 \dots

Schritte zur Lösung

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

Vereinfache

= \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

sum from n=1 to infinity of 4^{1/(2^n)}

n = 1 \sum \infty 4^{\frac{1}{2 ^{n}}}

derivative y=(2^x)^8

d er i v a t i v e y = (2^{x})^{8}

integral of (x^2+2)^42x

\int (x^{2} + 2)^{4} 2 x d x

4y^{''}+4y^'+8y=0

4 y^{^{''}} + 4 y^{^{'}} + 8 y = 0

limit as x approaches 0 of cos(9x)

x \to 0 lim (cos (9 x))