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Beliebt Rechnen >

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

Lösung

\int_{0}^{2 π} π cos^{2} (x) d x

Lösung

π^{2}

+1

Dezimale

9.86960 \dots

Schritte zur Lösung

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

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= π \cdot \int_{0}^{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

= π \frac{1}{2} \cdot \int_{0}^{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

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

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} cos (2 x) d x = 0

= π \frac{1}{2} (2 π + 0)

Vereinfache

π \frac{1}{2} (2 π + 0) : π^{2}

= π^{2}

Graph

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