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

Lösung

\int_{0}^{2 π} (1 - sin (x))^{2} d x

3 π

Dezimale

9.42477 \dots

Schritte zur Lösung

\int_{0}^{2 π} (1 - sin (x))^{2} d x

Multipliziere aus

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

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

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} 2 sin (x) d x = 0

\int_{0}^{2 π} sin^{2} (x) d x = π

= 2 π - 0 + π

Vereinfache

= 3 π

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