integral from 0 to pi of (1-cos(x))^2

Lösung

\int_{0}^{π} (1 - cos (x))^{2} d x

π + \frac{π}{2}

Dezimale

4.71238 \dots

Schritte zur Lösung

\int_{0}^{π} (1 - cos (x))^{2} d x

Multipliziere aus

(1 - cos (x))^{2} : 1 - 2 cos (x) + cos^{2} (x)

= \int_{0}^{π} 1 - 2 cos (x) + 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

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

\int_{0}^{π} 1 d x = π

\int_{0}^{π} 2 cos (x) d x = 0

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

= π - 0 + \frac{π}{2}

Vereinfache

= π + \frac{π}{2}

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