The area bounded by the curve $$y=|x-2|, x=1, x=3$$ and $$X$$-axis is

If $$\mathrm{f}^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2} < x < \frac{\pi}{2}$$ and $$f(0)=0$$, then $$\mathrm{f}(1)$$ is

The area bounded by the curves $$y=(x-1)^2, y=(x+1)^2$$ and $$y=\frac{1}{4}$$ is

If a curve $$y=a \sqrt{x}+b x$$ passes through the point $$(1,2)$$ and the area bounded by the curve, line $$x=4$$ and $$X$$-axis is 8 sq units, then