The area bounded by $x^2 + y^2 - 2x = 0$ and $y = \sin \frac{\pi x}{2}$ in the upper half of the circle is:

The area of the region bounded by the curve $y = x^2 + 2$ and the lines $y = x$,$x = 0$,and $x = 3$ is

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

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

The ratio in which the $x$-axis divides the area of the region bounded by the curves $y = x^2 - 4x$ and $y = 2x - x^2$ 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 $\frac{256A}{\pi}$.