integral from 0 to (2pi)/w of tsin(wt)

Lösung

\int_{0}^{\frac{2 π}{w}} t sin (wt) d t

- \frac{2 π}{w ^{2}}

Schritte zur Lösung

\int_{0}^{\frac{2 π}{w}} t sin (wt) d t

Wende die partielle Integration an

= [- \frac{1}{w} t cos (wt) - \int - \frac{1}{w} cos (wt) d t]_{0}^{\frac{2 π}{w}}

\int - \frac{1}{w} cos (wt) d t = - \frac{1}{w ^{2}} sin (wt)

= [- \frac{1}{w} t cos (wt) - (- \frac{1}{w ^{2}} sin (wt))]_{0}^{\frac{2 π}{w}}

Vereinfache

= [- \frac{1}{w} t cos (wt) + \frac{1}{w ^{2}} sin (wt)]_{0}^{\frac{2 π}{w}}

Berechne die Grenzen:

- \frac{2 π}{w ^{2}}

= - \frac{2 π}{w ^{2}}

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