For $x \in [0, 2\pi]$,the area of the region bounded by the curves $y = x + \sin x$ and $y = x$ is:

The area of the region bounded by $y-x=2$ and $x^{2}=y$ is equal to:

The area enclosed by $y^{2}=8x$ and $y=\sqrt{2}x$ that lies outside the triangle formed by $y=\sqrt{2}x$,$x=1$,and $y=2\sqrt{2}$ is equal to

The area of the region (in sq. units) enclosed between the curves $y=|x|$,$y=[x]$ and the ordinates $x=-1$,$x=0$,$x=1$ is

The area bounded by the parabolas $y=4x^{2}$, $y=\frac{x^{2}}{9}$ and the straight line $y=2$ 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: