Application of ...

The area bounded by the curve $$y^2 =4x$$ and the circle $$x^2 + y^2 -2x -3=0$$ is 

The area of the region defined by $$1 \leq \mid x-2 \mid + \mid y+ 1 \mid \leq 2$$ is

The area of the region defined by $$ \mid \mid x \mid - \mid y \mid \mid \leq 1 $$  and $$ x^2  + y^2 \leq 1 $$ in the $$xy$$ plane is

If the length of latus rectum of ellipse
$$ E_1 : 4(x+y-1)^2 + 2(x-y+3)^2 =8 $$
and $$ E_2: \dfrac{x^2}{p} + \dfrac{y^2}{p^2}=1, \ (0< p<1)$$ are equal, then area of ellipse $$ E_2, $$ is

If $$f(x)=x-1$$ and $$g(x) = \mid f( \mid x \mid ) - 2 \mid$$, then the area bounded by $$y=g(x)$$ and the curve $$x^2 -4y+8=0$$ is equal to

Area bounded by the ellipse $$ \dfrac{x^2}{4} + \dfrac{y^2}{9} =1$$ is equal to

A point $$P$$ lying inside the curve $$y= \sqrt{2ax-x^2}$$ is moving such that its shortest distance from the curve at any position is greater than its distance from $$X-$$axis. The point $$P$$ enclose a region whose area is equal to

Then, the absolute area enclosed by $$y=f(x)$$ and $$y=g(x)$$ is given by

The area bounded by $$y=2- \mid 2-x \mid$$ and $$y= \dfrac{3}{\mid x \mid}$$ is

Area bounded by $$y=f^{-1}(x)$$ and tangent and normal drawn to it at the points with abscissae $$\pi$$ and $$2 \pi$$, where $$f(x)=sin x- x$$ is