If the area of the region $\{(x, y) : |x-5| \leq y \leq 4 \sqrt{x}\}$ is $A$,then $3A$ is equal to . . . . . . .

The figure shows a portion of the graph $y=2x-4x^3$. The line $y=c$ is such that the areas of the regions marked $I$ and $II$ are equal. If $a$ and $b$ are the $x$-coordinates of $A$ and $B$ respectively,then $a+b$ equals:

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

If $(\alpha, \beta)$ is the stationary point of the curve $y=2x-x^2$,then the area bounded by the curves $y=2^x, y=2x-x^2, x=0$ and $x=\alpha$ is

If the area of the region $\{(x, y): x^{2/3} + y^{2/3} \leq 1, x + y \geq 0, y \geq 0\}$ is $A$,then find the value of $\frac{256A}{\pi}$.

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 $......$.