I'm learning integrals and I'm having trouble with evaluating this one:
$ \int_0^{8 \pi} \sqrt{ 4 - 4 \cos(t)} \mathrm{d} t $
The end result is $32 \sqrt{2}$.
I tried this by changing the form of the integral to
$\sqrt{8 \cdot \sin^2(t/2)}$
but I can't get the end result, which I specified above.
Any help is greatly appreciated, especially if explained in steps.