The area of the shaded region is ... sq. units.

The area bounded by the curves $y=x^2$ and $y-6=-|x|$ is

If the area enclosed by the parabolas $P_1: 2y = 5x^2$ and $P_2: x^2 - y + 6 = 0$ is equal to the area enclosed by $P_1$ and the line $y = \alpha x$,where $\alpha > 0$,then $\alpha^3$ is equal to $......$.

$OABC$ is a unit square where $O$ is the origin and $B=(1,1)$. The curves $y^2=x$ and $x^2=y$ divide the area of the square into three parts $a_1, a_2, a_3$. If $a_1, a_2, a_3$ are the areas (in sq units) of these parts respectively,then $a_1+2a_2+3a_3=$

The area (in $sq. \, units$) of the region bounded by the curves $x^{2}+2y-1=0$,$y^{2}+4x-4=0$,and $y^{2}-4x-4=0$ in the upper half plane is $....$

The area of the region bounded by the parabola $y=x^{2}-4x+5$ and the straight line $y=x+1$ is