integral from (-pi)/2 to pi/2 of xcos(x)

Lösung

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

0

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

0

= 0

\int_{- π}^{2 x} \frac{1}{1 + x ^{4}} d x

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