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

The area of the region $\{(x, y) : y \geq x^2 \text{ and } y \leq |x|\}$ is

The area (in sq.units) of the region bounded by the curve $y = \cos x$ between $x = -\frac{\pi}{2}, x = \frac{\pi}{2}$ and the x-axis is

If the area bounded by curves $y = 2^{kx}$, $x = 0$, $x = 2$ in first quadrant is $\frac{3}{\log 2}$, then $k$ is ($k \neq 0$)

The area (in Sq. units) of the region bounded by $y = -2$, $y = 2$, $x = y^3$ and $x = 0$ is equal to

The line $y = mx$ ($m > 0$) partitions the area of the circle $x^2 + y^2 = a^2$ ($a > 0$) in the ratio:

The area (in sq. units) bounded by a parabola $y^2=4x$ and its latus rectum, is