Application of ...

The function $$\displaystyle \mathrm{f}(\mathrm{x})=\max$$ $$\{x^{2},(1-x)^{2},2x(1-x) \forall 0\leq x \leq 1\}$$ then area of the region bounded by the curve $$\mathrm{y}=\mathrm{f}(\mathrm{x})$$ , $$\mathrm{x}$$-axis and $$\mathrm{x}= 0,\ \mathrm{x} =$$ 1 is equals

The ratio in which the area bounded by the curves $$y^2=12x $$ and $$x^2=12y$$ is divided by the line x $$=$$ 3 is

Find the area enclosed between the curves $$y^2- 2ye^{sin^{- 1}x} + x^2- 1 +[x] +e^{2sin^{- 1}x} = 0$$ 

If $$A_1$$ is the area bounded by $$y= \cos x, y = \sin x$$ &  $$x=0$$  and $$A_2$$ the area bounded by $$y = \cos x , y = \sin x , y = 0$$ in $$(0,\frac{\pi}{2})$$ then $$\displaystyle  \dfrac{A_1}{A_2}$$ equals to :

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

If $$\left| z- (4 + 4i) \right| \geq  4$$, then area of the region bounded by the locii of $$z,\; iz,\; - z$$ and $$-iz$$ is:

If the area bounded by the curve $$y = f(x)$$, the coordinate axes and the line $$x = x_1$$ is given by $$x_1e^{x_1}$$. Then $$f(x)$$ equals

If the area bounded by the curve $$|y|=sin^{-1}|x|$$ and  $$x=1$$ is $$a(\pi+b)$$, then the value $$a-b$$ is:

Area of the region bounded by the curve $$y = x^{2}$$ and $$y = sec^{-1} [sin^{2}x]$$ (where [ . ] denotes the greatest integer function) is

The area bounded by $$y=\sec^ {-1}{x}, y= \text{cosec}^{-1}{x}$$ and the line $$x-1=0$$ is: