integral from 0 to 2pi of xsin(x/2)

Lösung

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

4 π

Dezimale

12.56637 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [- 2 x cos (\frac{x}{2}) - \int - 2 cos (\frac{x}{2}) d x]_{0}^{2 π}

\int - 2 cos (\frac{x}{2}) d x = - 4 sin (\frac{x}{2})

= [- 2 x cos (\frac{x}{2}) - (- 4 sin (\frac{x}{2}))]_{0}^{2 π}

Vereinfache

= [- 2 x cos (\frac{x}{2}) + 4 sin (\frac{x}{2})]_{0}^{2 π}

Berechne die Grenzen:

4 π

= 4 π

\int_{1}^{2} x e^{\frac{x}{2}} d x

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