Evaluate integral:
$$\int_{0}^{2\pi} \sqrt{\frac{1-\cos x}{2}} dx$$
I don't even know where to begin, was absent from class the day of this lecture. I know I'm supposed to use some identity related to $$1+\cos2\theta = 2\cos^2\theta$$ but I'm sort of lost. Any help would be appreciated.
Best Answer
Hint. You may use $$ \sin^2 \frac{x}2=\frac{1-\cos x}2 $$ and $\sin u \geq0, \, u \in [0,\pi].$