The area of the region bounded by the curves $x + 3y^2 = 0$ and $x + 4y^2 = 1$ is equal to: (in $/3$)

The area of the region $A = \{(x, y): 4x^2 + y^2 \le 8 \text{ and } y^2 \le 4x\}$ is:

The area of the region inside the circle $(x-2 \sqrt{3})^2+y^2=12$ and outside the parabola $y^2=2 \sqrt{3} x$ is

The area enclosed by the curves $y = \sin^{-1}(\cos x)$ and $y = \cos^{-1}(\sin x)$ for $x \in \left[ \frac{\pi}{2}, \frac{3\pi}{2} \right]$ is:

The area of the region $\{(x, y): x^2 \leq y \leq 8-x^2, y \leq 7\}$ is

The following figure shows the graph of a continuous function $y=f(x)$ on the interval $[1,3]$. The points $A, B, C$ have coordinates $(1,1), (3,2), (2,3)$ respectively,and the lines $l_1$ and $l_2$ are parallel,with $l_1$ being tangent to the curve at $C$. If the area under the graph of $y=f(x)$ from $x=1$ to $x=3$ is $4$ sq units,then the area of the shaded region is