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Beliebt Rechnen >

integral from 0 to pi/6 of (1-cos(3x))sin(3x)

Lösung

\int_{0}^{\frac{π}{6}} (1 - cos (3 x)) sin (3 x) d x

Lösung

\frac{1}{6}

+1

Dezimale

0.16666 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{6}} (1 - cos (3 x)) sin (3 x) d x

Wende U-Substitution an

= \int_{0}^{1} \frac{u}{3} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{0}^{1} u d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{u ^{2}}{2}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= \frac{1}{3} \cdot \frac{1}{2}

Vereinfache

= \frac{1}{6}

Graph

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