integral from 0 to pi of θsin(θ)

Lösung

\int_{0}^{π} θ sin (θ) d θ

π

Dezimale

3.14159 \dots

Schritte zur Lösung

\int_{0}^{π} θ sin (θ) d θ

Wende die partielle Integration an

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

\int - cos (θ) d θ = - sin (θ)

= [- θ cos (θ) - (- sin (θ))]_{0}^{π}

Vereinfache

= [- θ cos (θ) + sin (θ)]_{0}^{π}

Berechne die Grenzen:

π

= π

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