integral from 0 to t of cos(2t)

Lösung

\int_{0}^{t} cos (2 t) d t

\frac{1}{2} sin (2 t)

Schritte zur Lösung

\int_{0}^{t} cos (2 t) d t

Wende U-Substitution an

= \int_{0}^{2 t} cos (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}^{2 t} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [sin (u)]_{0}^{2 t}

Berechne die Grenzen:

sin (2 t)

= \frac{1}{2} sin (2 t)

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