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 ?

What is $$\int_{{e^{ - 1}}}^{{e^2}} {\left| {{{\ln x} \over x}} \right|} dx$$ equal to ?

What is $$\int_a^b {[x]dx + \int_a^b {[ - x]dx} } $$ equal to, where [ , ] is the greatest integer function?