Let $A$ be the area of the region $\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2x(1-x)\}$. Then $540A$ is equal to

The area bounded by the curves $y=\frac{1}{4}\left|4-x^2\right|$ and $y=7-|x|$ is

If the area of the region bounded by the curves $y=4-\frac{x^2}{4}$ and $y=\frac{x-4}{2}$ is equal to $\alpha$,then $6 \alpha$ equals

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 enclosed between the curves $y = x^3$ and $y = \sqrt{x}$ is,(in square units)

The volume of the solid generated by revolving about the $y-$axis the figure bounded by the parabolas $y = x^2$ and $x = y^2$ is