integral from 0 to pi of xsin(4x)

Lösung

\int_{0}^{π} x sin (4 x) d x

- \frac{π}{4}

Dezimale

- 0.78539 \dots

Schritte zur Lösung

\int_{0}^{π} x sin (4 x) d x

Wende die partielle Integration an

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

\int - \frac{1}{4} cos (4 x) d x = - \frac{1}{16} sin (4 x)

= [\frac{1}{4} (- x cos (4 x) - 4 (- \frac{1}{16} sin (4 x)))]_{0}^{π}

Vereinfache

[\frac{1}{4} (- x cos (4 x) - 4 (- \frac{1}{16} sin (4 x)))]_{0}^{π} : [\frac{1}{4} (- x cos (4 x) + \frac{1}{4} sin (4 x))]_{0}^{π}

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

Berechne die Grenzen:

- \frac{π}{4}

= - \frac{π}{4}

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