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

Lösung

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

1

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} x sin (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

1

= 1

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