Area of the region bounded by two parabolas $y=x^{2}$ and $x=y^{2}$ is

The area of the region bounded by the curves $y=9x^2$ and $y=5x^2+4$ (in sq units) is

The positive values of the parameter $a$ for which the area of the figure bounded by the curve $y = \cos ax$,$y = 0$,$x = \frac{\pi}{6a}$,and $x = \frac{5\pi}{6a}$ is greater than $3$ are:

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:

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

The area (in sq. units) of the smaller region lying above the $X$-axis and bounded between the circle $x^2+y^2=2ax$ and the parabola $y^2=ax$ is