integral from 0 to kpi of xsin(x)

Lösung

\int_{0}^{kπ} x sin (x) d x

sin (πk) - πk cos (πk)

Schritte zur Lösung

\int_{0}^{kπ} x sin (x) d x

Wende die partielle Integration an

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

\int - cos (x) d x = - sin (x)

= [- x cos (x) - (- sin (x))]_{0}^{πk}

Vereinfache

= [- x cos (x) + sin (x)]_{0}^{πk}

Berechne die Grenzen:

sin (πk) - πk cos (πk)

= sin (πk) - πk cos (πk)

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