The area bounded by the curves $y = x(x - 3)^2$ and $y = x$ is (in sq. units) :

The area bounded by the curves $y^2 = 4x$ and $x^2 = 4y$ is

The area of the region bounded by the curves $y=9x^2$ and $y=5x^2+4$ (in sq units) is

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 enclosed by the curves $y = \cos x$,$y = 1 + \sin 2x$ and $x = \frac{3\pi}{2}$ in the first and fourth quadrants (as shown in the figure) is:

The area enclosed by the curves $xy + 4y = 16$ and $x + y = 6$ is equal to: