Let $$\,{y^2} - 2y + 1 = x$$ and $$\,\sqrt x + y = 5.\,\,$$ The value of $$\,x + \sqrt y \,\,$$ equals ________. (Given the answer up to three decimal places)

Let $${\rm I} = c\int {\int {_Rx{y^2}dxdy,\,\,} } $$ where $$R$$ is the region shown in the figure and $$c = 6 \times {10^{ - 4}}.\,\,$$ The value of $${\rm I}$$ equals ___________.

The maximum value attained by the function $$f(x)=x(x-1) (x-2)$$ in the interval $$\left[ {1,2} \right]$$ is _________.

A particle, starting from origin at $$t=0$$ $$s,$$ is traveling along $$x$$-axis with velocity $$v = {\pi \over 2}\cos \left( {{\pi \over 2}t} \right)m/s$$
At $$t=3$$ $$s,$$ the difference between the distance covered by the particle and the magnitude of displacement from the origin is _________.