Application of ...

The are included between the curves $$y^2 = 4ax \,$$ and $$\, x^2 = 4 ay$$ is ____  sq units.

The area of the region enclosed by the curves $$y=x$$, $$x=e$$, $$y=\dfrac{1}{x}$$ and the positive $$x-axis$$ is . 

The area bounded by the curve $$y=cos ax$$ in one are of the curve is where $$a=4n+1,n\in integer$$

Area enclosed between the curves $$\left| y \right| = 1 - {x^2}$$ and $${x^2} + {y^2} = 1$$ is 

The area bounded by the curves $$y=xe, y=-xe$$ and the line $$x=1$$ is-

The area bounded by the curves $$y=|x|-1$$ and $$y=-|x|+1$$ is?

Area bounded by curve $$y = k \sin \,x$$ between $$x = \pi$$ and $$x = 2\pi$$, is

Suppose that $$F(\alpha)$$ denotes the area of the region bounded by $$x=0$$, $$x=2$$, $$y^2=4x$$ and $$y=|\alpha x-1|+|\alpha x-2|+\alpha x$$, where $$\alpha \in \{0, 1\}$$. Then the value of $$F(\alpha)+\dfrac{8\sqrt{2}}{3}$$, when $$\alpha =0$$, is

The area bounded by the curves $$x^2=4ay$$ and $$y^2=4ax$$ is,

The area of the region bounded by the curves $$y=x^2 $$ and $$y = \dfrac {2}{1+x^2} $$ is :