integral from 0 to 4pi of sin(2x)

Lösung

\int_{0}^{4 π} sin (2 x) d x

0

Schritte zur Lösung

\int_{0}^{4 π} sin (2 x) d x

Wende U-Substitution an

= \int_{0}^{8 π} sin (u) \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{8 π} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [- cos (u)]_{0}^{8 π}

Berechne die Grenzen:

0

= \frac{1}{2} \cdot 0

Vereinfache

= 0

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