integral from 0 to pi of (2+cos(θ))^2

Lösung

\int_{0}^{π} (2 + cos (θ))^{2} d θ

4 π + \frac{π}{2}

Dezimale

14.13716 \dots

Schritte zur Lösung

\int_{0}^{π} (2 + cos (θ))^{2} d θ

Multipliziere aus

(2 + cos (θ))^{2} : 4 + 4 cos (θ) + cos^{2} (θ)

= \int_{0}^{π} 4 + 4 cos (θ) + cos^{2} (θ) d θ

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} 4 d θ + \int_{0}^{π} 4 cos (θ) d θ + \int_{0}^{π} cos^{2} (θ) d θ

\int_{0}^{π} 4 d θ = 4 π

\int_{0}^{π} 4 cos (θ) d θ = 0

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

= 4 π + 0 + \frac{π}{2}

Vereinfache

= 4 π + \frac{π}{2}

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