The area of the region enclosed by the parabolas $y=x^2-5x$ and $y=7x-x^2$ is:

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 $x = 0, y = 0, x = 2, y = 2, y \leq e^x$ and $y \geq \log x$ is

The area bounded by the curves $y=\frac{1}{4}\left|4-x^2\right|$ and $y=7-|x|$ 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

The area (in sq. units) of the portion lying above the $X$-axis and enclosed between the curves $y^2=2ax-x^2$ and $y^2=ax$ is