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

Lösung

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

2 π - 4 + \frac{π}{4}

Dezimale

3.06858 \dots

Schritte zur Lösung

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

Multipliziere aus

(2 - sin (x))^{2} : 4 - 4 sin (x) + sin^{2} (x)

= \int_{0}^{\frac{π}{2}} 4 - 4 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}^{\frac{π}{2}} 4 d x - \int_{0}^{\frac{π}{2}} 4 sin (x) d x + \int_{0}^{\frac{π}{2}} sin^{2} (x) d x

\int_{0}^{\frac{π}{2}} 4 d x = 2 π

\int_{0}^{\frac{π}{2}} 4 sin (x) d x = 4

\int_{0}^{\frac{π}{2}} sin^{2} (x) d x = \frac{π}{4}

= 2 π - 4 + \frac{π}{4}

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