integral from 0 to pi/6 of sin(6x)

Lösung

\int_{0}^{\frac{π}{6}} sin (6 x) d x

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{6}} sin (6 x) d x

Wende U-Substitution an

= \int_{0}^{π} sin (u) \frac{1}{6} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{0}^{π} sin (u) d u

Nutze das gemeinsame Integral :

\int sin (u) d u = - cos (u)

= \frac{1}{6} [- cos (u)]_{0}^{π}

Berechne die Grenzen:

2

= \frac{1}{6} \cdot 2

Vereinfache

= \frac{1}{3}

\int_{0}^{2} - x^{2} + 2 x d x

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