Find the area of the region bounded by the two parabolas $y=x^{2}$ and $y^{2}=x$.

The area of the region bounded by the curves $y=x^3$, $y=x^2$ and the lines $x=0$ and $x=2$ is

The area (in sq. units) bounded by the curves $y=\frac{8}{x}$,$y=2x$ and $x=4$ is

The area bounded by the curves $y=|x-1|+|x-2|$ and $y=3$ is equal to

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

The area of the region bounded by the curves $y=x^{3}$, $y=\frac{1}{x}$, and the line $x=2$ in the first quadrant is: