Let the area of the region $\{(x, y) : |2x - 1| \leq y \leq |x^2 - x|, 0 \leq x \leq 1\}$ be $A$. Then $(6A + 11)^2$ is equal to $.......$.

For $a>0$, let the curves $C_1: y^2=a x$ and $C _2: x ^2=$ ay intersect at origin O and a point P Let the line $x = b (0 < b < a )$ intersect the chord $O P$ and the x -axis at points Q and R , respectively. If the line $x=b$ bisects the area bounded by the curves, $C _1$ and $C _2$, and the area of $\Delta OQR =\frac{1}{2}$, then ' $a$ ' satisfies the equation

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

If the area of the circle $x^2+y^2=2$ is divided into two parts by the parabola $y=x^2$,then the area (in sq units) of the larger part is

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 (in sq. units) bounded by the curves $y=\sqrt{x}$,$2y-x+3=0$,$X$-axis and lying in the first quadrant,is