The area (in square units) of the region bounded by the curves $y + 2x^2 = 0$ and $y + 3x^2 = 1$ is equal to

The area of the region bounded by the parabola $y=x^2$ and the curve $y=|x|$ is

Let $A_{1}=\{(x, y):|x| \leq y^{2},|x|+2 y \leq 8\}$ and $A_{2}=\{(x, y):|x|+|y| \leq k\}$. If $27 \times \text{Area}(A_{1}) = 5 \times \text{Area}(A_{2})$,then $k$ is equal to

What is the area bounded by the curves $x^2 + y^2 = 9$ and $y^2 = 8x$?

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:

The area (in sq. units) of the region bounded by the parabola $y = x^2 + 2$ and the lines $y = x + 1$,$x = 0$,and $x = 3$ is: