The volume of a solid obtained by revolving about the $y$-axis the region enclosed between the ellipse $x^2 + 9y^2 = 9$ and the straight line $x + 3y = 3$ in the first quadrant is: (in $\pi$)

The area (in square units) of the region bounded by the parabola $y^2=4(x-2)$ and the line $y=2x-8$ 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 bounded by the parabola $y^2 = 4x$ and the line $2x - 3y + 4 = 0$,in square units,is

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

Let $C_{1}$ be the curve obtained by the solution of the differential equation $2xy \frac{dy}{dx} = y^{2} - x^{2}, x > 0$. Let the curve $C_{2}$ be the solution of $\frac{2xy}{x^{2} - y^{2}} = \frac{dy}{dx}$. If both the curves pass through $(1, 1)$,then the area enclosed by the curves $C_{1}$ and $C_{2}$ is equal to: