The area (in sq. units) of the region bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is

Let $a$ and $b$ respectively be the points of local maximum and local minimum of the function $f(x)=2 x^{3}-3 x^{2}-12 x$. If $A$ is the total area of the region bounded by $y=f(x)$,the $x$-axis and the lines $x=a$ and $x=b$,then $4 A$ is equal to ..... .

The area of the plane region bounded by the curves $x + 2y^2 = 0$ and $x + 3y^2 = 1$ is equal to

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

Let the area of the region enclosed by the curve $y = \min \{\sin x, \cos x\}$ and the $x$-axis between $x = -\pi$ to $x = \pi$ be $A$. Then $A^2$ is equal to...........

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 $......$.