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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{π ^{2}}{4}

+1

Dezimale

2.46740 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= π \cdot \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

= π \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

= π \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

= π \frac{1}{2} (\frac{π}{2} + 0)

Vereinfache

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

= \frac{π ^{2}}{4}

Graph

Beliebte Beispiele

integral of (x+9)/(x^2+4)

\int \frac{x + 9}{x ^{2} + 4} d x

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x \to \infty lim ((x!)^{2})

fläche x^2-12,4x

a re a x^{2} - 12, 4 x

normal y=(x+3)^3,\at x=-1/75

n or ma l y = (x + 3)^{3}, at x = - \frac{1}{75}

derivative of 2/((2-x^2))

\frac{d}{d x} (\frac{2}{( 2 - x ) ^{2}})