For any real number x, let [ x ] denote the largest integer less than or equal to x. If $$I = \int\limits_0^{10} {\left[ {\sqrt {{{10x} \over {x + 1}}} } \right]dx} $$, then the value of 9I is __________.

Let $$f:R \to R$$ be a differentiable function such that its derivative f' is continuous and f($$\pi $$) = $$-$$6.

If $$F:[0,\pi ] \to R$$ is defined by $$F(x) = \int_0^x {f(t)dt} $$, and if $$\int_0^\pi {(f'(x)} + F(x))\cos x\,dx$$ = 2

then the value of f(0) is ...........

The value of the integral $$ \int\limits_0^{\pi /2} {{{3\sqrt {\cos \theta } } \over {{{(\sqrt {\cos \theta } + \sqrt {\sin \theta } )}^5}}}} d\theta $$ equals ..............

If $$I = {2 \over \pi }\int\limits_{ - \pi /4}^{\pi /4} {{{dx} \over {(1 + {e^{\sin x}})(2 - \cos 2x)}}} $$, then 27I² equals .................