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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{π}{4}

+1

Dezimale

0.78539 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

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 t) d t

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

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

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

limit as x approaches 0+of x^2+4

x \to 0 + lim (x^{2} + 4)

integral of xe^e

\int x e^{e} d x

integral from 5 to 5 of 10x^4

\int_{5}^{5} 10 x^{4} d x

(d^2)/(dx^2)(((x-4)(x^2+4x+16))/(x^3))

\frac{d ^{2}}{d x ^{2}} (\frac{( x - 4 ) ( x ^{2} + 4 x + 16 )}{x ^{3}})

(dy)/(dx)=10sqrt(x)y

\frac{d y}{d x} = 10 x y