integral from 0 to x/2 of sin(2t)

Lösung

\int_{0}^{\frac{x}{2}} sin (2 t) d t

\frac{1}{2} (- cos (x) + 1)

Schritte zur Lösung

\int_{0}^{\frac{x}{2}} sin (2 t) d t

Wende U-Substitution an

= \int_{0}^{x} 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}^{x} sin (u) d u

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

- cos (x) + 1

= \frac{1}{2} (- cos (x) + 1)

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