integral from 0 to pi/2 of x*cos(x)

Lösung

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

\frac{π}{2} - 1

Dezimale

0.57079 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} x cos (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

\frac{π}{2} - 1

= \frac{π}{2} - 1

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