integral from 0 to pi/3 of xsin(6x)

Lösung

\int_{0}^{\frac{π}{3}} x sin (6 x) d x

- \frac{π}{18}

Dezimale

- 0.17453 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{3}} 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}{3}}

\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}{3}}

Vereinfache

[\frac{1}{6} (- x cos (6 x) - 6 (- \frac{1}{36} sin (6 x)))]_{0}^{\frac{π}{3}} : [\frac{1}{6} (- x cos (6 x) + \frac{1}{6} sin (6 x))]_{0}^{\frac{π}{3}}

= [\frac{1}{6} (- x cos (6 x) + \frac{1}{6} sin (6 x))]_{0}^{\frac{π}{3}}

Berechne die Grenzen:

- \frac{π}{18}

= - \frac{π}{18}

\int (1 + x)^{0} d x

\frac{d}{d x} (x - (\frac{1}{2})^{x})

\int cos^{3} (θ) + cos (θ) sin^{2} (θ) d θ

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