Consider a region R = {(x, y) $$ \in $$ R : x² $$ \le $$ y $$ \le $$ 2x}. if a line y = $$\alpha $$ divides the area of region R into two equal parts, then which of the following is true?

Area (in sq. units) of the region outside

$${{\left| x \right|} \over 2} + {{\left| y \right|} \over 3} = 1$$ and inside the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$$ is :

Given : $$f(x) = \left\{ {\matrix{ {x\,\,\,\,\,,} & {0 \le x < {1 \over 2}} \cr {{1 \over 2}\,\,\,\,,} & {x = {1 \over 2}} \cr {1 - x\,\,\,,} & {{1 \over 2} < x \le 1} \cr } } \right.$$

and $$g(x) = \left( {x - {1 \over 2}} \right)^2,x \in R$$

Then the area (in sq. units) of the region bounded by the curves, y = ƒ(x) and y = g(x) between the lines, 2x = 1 and 2x = $$\sqrt 3 $$, is :

The area (in sq. units) of the region

{(x,y) $$ \in $$ R² : x² $$ \le $$ y $$ \le $$ 3 – 2x}, is :