integral from 0 to pi of sqrt(sin(θ))

Lösung

\int_{0}^{π} sin (θ) d θ

- 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - π) ∣) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣)

Schritte zur Lösung

\int_{0}^{π} sin (θ) d θ

Das ist ein nicht elementares Integral :

\int sin (x) d x = - 2 E (\frac{1}{2} (\frac{π}{2} - x) ∣ 2)

= [- 2 E (\frac{1}{2} (\frac{π}{2} - θ) ∣ 2)]_{0}^{π}

Berechne die Grenzen:

- 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - π) ∣) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣)

= - 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - π) ∣) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣)

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