integral of (1-cos(2x))^{1/2}

Lösung

\int (1 - cos (2 x))^{\frac{1}{2}} d x

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

Schritte zur Lösung

\int (1 - cos (2 x))^{\frac{1}{2}} d x

Vereinfache

(1 - cos (2 x))^{\frac{1}{2}} : 2^{\frac{1}{2}} sin (x)

= \int 2^{\frac{1}{2}} sin (x) d x

Entferne die Konstante:

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

= 2^{\frac{1}{2}} \cdot \int sin (x) d x

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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