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 ?

If f(x) and g(x) are continuous functions satisfying f(x) = f(a $$-$$ x) and g(x) + g(a $$-$$ x) = 2, then what is $$\int_0^a {f(x)g(x)dx} $$ equal to ?