integral from pi/6 to pi/2 of xcos(x)

Lösung

\int_{\frac{π}{6}}^{\frac{π}{2}} x cos (x) d x

\frac{5 π - 6 3}{12}

Dezimale

0.44297 \dots

Schritte zur Lösung

\int_{\frac{π}{6}}^{\frac{π}{2}} x cos (x) d x

Wende die partielle Integration an

= [x sin (x) - \int sin (x) d x]_{\frac{π}{6}}^{\frac{π}{2}}

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

= [x sin (x) - (- cos (x))]_{\frac{π}{6}}^{\frac{π}{2}}

Vereinfache

= [x sin (x) + cos (x)]_{\frac{π}{6}}^{\frac{π}{2}}

Berechne die Grenzen:

\frac{5 π - 6 3}{12}

= \frac{5 π - 6 3}{12}

\int_{0}^{π} cos (\frac{1}{2} x) d x

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