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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{π}{4}

+1

Dezimale

0.78539 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

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

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

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

= \frac{1}{2} (π - \frac{π}{2} + 0)

Vereinfache

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

= \frac{π}{4}

Graph

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