integral from 0 to pi/6 of xsin(6x)

Lösung

\int_{0}^{\frac{π}{6}} x sin (6 x) d x

\frac{π}{36}

Dezimale

0.08726 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{6}} x sin (6 x) d x

Wende die partielle Integration an

= [\frac{1}{6} (- x cos (6 x) - 6 \cdot \int - \frac{1}{6} cos (6 x) d x)]_{0}^{\frac{π}{6}}

\int - \frac{1}{6} cos (6 x) d x = - \frac{1}{36} sin (6 x)

= [\frac{1}{6} (- x cos (6 x) - 6 (- \frac{1}{36} sin (6 x)))]_{0}^{\frac{π}{6}}

Vereinfache

[\frac{1}{6} (- x cos (6 x) - 6 (- \frac{1}{36} sin (6 x)))]_{0}^{\frac{π}{6}} : [\frac{1}{6} (- x cos (6 x) + \frac{1}{6} sin (6 x))]_{0}^{\frac{π}{6}}

= [\frac{1}{6} (- x cos (6 x) + \frac{1}{6} sin (6 x))]_{0}^{\frac{π}{6}}

Berechne die Grenzen:

\frac{π}{36}

= \frac{π}{36}