$\int_2^5 (\sqrt{x+2 \sqrt{x-1}} + \sqrt{x-2 \sqrt{x-1}}) dx = $ (in $/3$)

The value of $\int_{3}^{4} \sqrt{(4-x)(x-3)} d x$ is

If $f : R \to R$ is a continuous function such that $f(x) = \int\limits_1^x {tf(t)dt}$,then the correct statement is -

If $\int_0^{\frac{\pi}{2}} \frac{\cot x}{\cot x + \csc x} dx = m(\pi + n)$,then $m \cdot n$ is equal to

If $[.]$ represents the greatest integer function,then evaluate the integral: $\int_{\frac{3 \pi}{4}}^\pi \left[ \sin x + \left[ \frac{4 x}{\pi} \right] \right] dx$.

$\int\limits_2^4 {\left[ {{{\log }_x}2 - \frac{{{{\left( {{{\log }_x}2} \right)}^2}}}{{\ln 2}}} \right]} dx =$