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Beliebt Rechnen >

integral from 0 to pi/5 of xsin(10x)

Lösung

\int_{0}^{\frac{π}{5}} x sin (10 x) d x

Lösung

- \frac{π}{50}

+1

Dezimale

- 0.06283 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{5}} x sin (10 x) d x

Wende die partielle Integration an

= [\frac{1}{10} (- x cos (10 x) - 10 \cdot \int - \frac{1}{10} cos (10 x) d x)]_{0}^{\frac{π}{5}}

\int - \frac{1}{10} cos (10 x) d x = - \frac{1}{100} sin (10 x)

= [\frac{1}{10} (- x cos (10 x) - 10 (- \frac{1}{100} sin (10 x)))]_{0}^{\frac{π}{5}}

Vereinfache

[\frac{1}{10} (- x cos (10 x) - 10 (- \frac{1}{100} sin (10 x)))]_{0}^{\frac{π}{5}} : [\frac{1}{10} (- x cos (10 x) + \frac{1}{10} sin (10 x))]_{0}^{\frac{π}{5}}

= [\frac{1}{10} (- x cos (10 x) + \frac{1}{10} sin (10 x))]_{0}^{\frac{π}{5}}

Berechne die Grenzen:

- \frac{π}{50}

= - \frac{π}{50}

Graph

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