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

The area (in sq. units) of the region $\{x \in R : x \ge 0, y \ge 0, y \ge x - 2, \text{ and } y \le \sqrt{x}\}$ is

The area of the region that is common to the circle $x^2+y^2=16a^2$ and the parabola $y^2=6ax$ is

The area bounded by the curve $y = |x^{2}-9|$ and the line $y = 3$ is

The parabolas $y^2 = 4x$ and $x^2 = 4y$ divide the square region bounded by the lines $x = 4$,$y = 4$ and the coordinate axes. If $S_1, S_2, S_3$ are respectively the areas of these parts numbered from top to bottom,then $S_1:S_2:S_3$ is

If the area enclosed by the parabolas $P_1: 2y = 5x^2$ and $P_2: x^2 - y + 6 = 0$ is equal to the area enclosed by $P_1$ and the line $y = \alpha x$,where $\alpha > 0$,then $\alpha^3$ is equal to $......$.