What is $$\int_0^{4\pi } {\left| {\cos x} \right|} \,dx$$ equal to ?

What is $$\int\limits_0^{2\pi } {\sqrt {1 + \sin {x \over 2}} dx} $$ equal to ?

The value of $$\int_0^{{\pi \over 4}} {\sqrt {\tan x} dx + \int_0^{{\pi \over 4}} {\sqrt {\cot x} dx} } $$ is equal to

What is $$\int_0^{{\pi \over 2}} {{{d\theta } \over {1 + \cos \theta }}} $$ equal to ?