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Beliebt Rechnen >

integral from 0 to 1 of cos^2(pix)

Lösung

\int_{0}^{1} cos^{2} (π x) d x

Lösung

\frac{1}{2}

+1

Dezimale

0.5

Schritte zur Lösung

\int_{0}^{1} cos^{2} (π x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int_{0}^{1} 1 - sin^{2} (π 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

= \int_{0}^{1} 1 d x - \int_{0}^{1} sin^{2} (π x) d x

\int_{0}^{1} 1 d x = 1

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

= 1 - \frac{1}{2}

Vereinfache

1 - \frac{1}{2} : \frac{1}{2}

= \frac{1}{2}

Graph

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