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Beliebt Rechnen >

integral of ((1+cos(3t))/2)

Lösung

\int (\frac{1 + cos ( 3 t )}{2}) d t

Lösung

\frac{1}{2} (t + \frac{1}{3} sin (3 t)) + C

Schritte zur Lösung

\int \frac{1 + cos ( 3 t )}{2} d t

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int 1 + cos (3 t) d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d t + \int cos (3 t) d t)

\int 1 d t = t

\int cos (3 t) d t = \frac{1}{3} sin (3 t)

= \frac{1}{2} (t + \frac{1}{3} sin (3 t))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (t + \frac{1}{3} sin (3 t)) + C

Graph

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