integral from 0 to pi/(12) of sin(6x)

Lösung

\int_{0}^{\frac{π}{12}} sin (6 x) d x

\frac{1}{6}

Dezimale

0.16666 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{12}} sin (6 x) d x

Wende U-Substitution an

= \int_{0}^{\frac{π}{2}} 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}^{\frac{π}{2}} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{6} [- cos (u)]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

1

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

Vereinfache

= \frac{1}{6}

\int_{- 1}^{2} \frac{3}{x ^{4}} d x

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