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Beliebt Rechnen >

integral from 0 to pi/4 of xsin(12x)

Lösung

\int_{0}^{\frac{π}{4}} x sin (12 x) d x

Lösung

\frac{π}{48}

+1

Dezimale

0.06544 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} x sin (12 x) d x

Wende die partielle Integration an

= [\frac{1}{12} (- x cos (12 x) - 12 \cdot \int - \frac{1}{12} cos (12 x) d x)]_{0}^{\frac{π}{4}}

\int - \frac{1}{12} cos (12 x) d x = - \frac{1}{144} sin (12 x)

= [\frac{1}{12} (- x cos (12 x) - 12 (- \frac{1}{144} sin (12 x)))]_{0}^{\frac{π}{4}}

Vereinfache

[\frac{1}{12} (- x cos (12 x) - 12 (- \frac{1}{144} sin (12 x)))]_{0}^{\frac{π}{4}} : [\frac{1}{12} (- x cos (12 x) + \frac{1}{12} sin (12 x))]_{0}^{\frac{π}{4}}

= [\frac{1}{12} (- x cos (12 x) + \frac{1}{12} sin (12 x))]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

\frac{π}{48}

= \frac{π}{48}

Graph

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