integral from pi/2 to pi of θsin(θ)

Lösung

\int_{\frac{π}{2}}^{π} θ sin (θ) d θ

π - 1

Dezimale

2.14159 \dots

Schritte zur Lösung

\int_{\frac{π}{2}}^{π} θ sin (θ) d θ

Wende die partielle Integration an

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

\int - cos (θ) d θ = - sin (θ)

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

Vereinfache

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

Berechne die Grenzen:

π - 1

= π - 1

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