Application of ...

The whole area of the curves $$x=a\cos^3t, y=b\sin^3t$$ is given by?

The area between the curves y=tan x, cot x and axis in the interval $$\left[0,\pi   \right/2$$]is ?

The area bounded by the curves $$y = \sin \left( {x - \left[ x \right]} \right),\,y = \sin 1$$ and the x-axis is

The area (in square units) bounded by the curves $$y = {\cos ^{ - 1}}\left| {\cos \,x} \right|$$ and $$y = {\left( {{{\cos }^{ - 1}}\left| {\cos \,x} \right|} \right)^2},x \in \left[ {0,\pi } \right]$$ is

The area bounded by the curves $$y = sin^{-1} |sin \, x| $$ and $$y = (sin^{-1} | sin \, x|)^2 , \, 0 \le x \le 2 \pi$$ is

The area bounded by the curves $${y^2} = 4x$$ and $${x^2} = 4y$$ is : 

The area bounded by $$y=2-\left| 2-x \right|$$ and $$y=\frac { 3 }{ \left| x \right|  }$$ is :

Area of the region defined by $$1\ \le |x|+|y|$$ and $$x^{2}-2x+1 \le 1-y^{2}$$ is $$k \pi$$ then $$k=.....sq$$ units 

The maximum area bounded by the curves $${y^2} = 4ax,\,\,\,\,y = ax\,\,a$$ and $$y = \frac{x}{a}\,\,,1 \le a \le 2$$  is 

Consider two curves $${C_1}\,:\,y = \frac{1}{x}\,and\,{C_2}:\,y = \,\ell nx$$  on the $$xy$$ plane. Let $${D_1}$$ denotes the region surrounded by $${C_1},{C_2}$$ and the lines $$x=1$$  and $${D_2}$$ denotes the region the region surrounded by $${C_1},{D_2}$$ and the line $$x=a$$. If a $${D_1}={D_2}$$ then the value of $$'a'$$ -