The area of the region bounded by $y^{2}=8x$ and $y^{2}=16(3-x)$ is equal to

The area (in square units) of the region enclosed by the ellipse $x^2+3y^2=18$ in the first quadrant below the line $y=x$ is:

The sine and cosine curves intersect infinitely many times,creating bounded regions of equal areas. The area of one such region is

Area of the region (in sq units) bounded by the curves $y=\sqrt{x}$, $x=\sqrt{y}$ and the lines $x=1$, $x=4$ is

Let $S$ be the region bounded by the curves $y=x^{3}$ and $y^{2}=x$. The curve $y=2|x|$ divides $S$ into two regions of areas $R_{1}$ and $R_{2}$. If $\max \{R_{1}, R_{2}\}=R_{2}$,then $\frac{R_{2}}{R_{1}}$ is equal to

The area (in sq. units) of the region lying in the first quadrant and enclosed by the $X$-axis,the straight line $x - \sqrt{3}y = 0$ and the circle $x^2 + y^2 = 4$ is