The area (in sq units) bounded by the curves $y^2=4x$ and $x^2=4y$ is

The area (in sq. units) of the region enclosed by the set of points ${(x, y) | y \leq x^2, xy \leq 8, y \geq 1}$ is...

The area (in square units) bounded by the curves $y=2x^2$ and $y=\max \{x-[x], x+|x|\}$ in between the lines $x=0$ and $x=2$ is

Let $S = \{(x, y) \in R \times R : x \geq 0, y \geq 0, y^2 \leq 4x, y^2 \leq 12 - 2x \text{ and } 3y + \sqrt{8}x \leq 5\sqrt{8}\}$. If the area of the region $S$ is $\alpha \sqrt{2}$,then $\alpha$ is equal to

The area of the region bounded by the curves $y^{2}=8x$ and $y=x$ is

The area (in sq. units) bounded by the curves $y=\sqrt{x}$,$2y-x+3=0$,$X$-axis and lying in the first quadrant,is