The area bounded between the parabola $y^{2}=4x$ and the line $y=2x-4$ is equal to

The area of the region bounded by the curve $y^2=9x$ and the line $y=3x$ is

Let $S(\alpha) = \{(x,y) : y^2 \leq x, 0 \leq x \leq \alpha\}$ and $A(\alpha)$ be the area of the region $S(\alpha)$. If for a $\lambda, 0 < \lambda < 4, A(\lambda) : A(4) = 2 : 5$,then $\lambda$ equals:

The area (in sq. units) bounded by the parabola $y=x^2+3$, the tangent to the parabola at $(3,12)$ and the coordinate axes and lying in the first quadrant is

The area of the region bounded by the curve $y=|x-5|$,the $X$-axis,and the lines $x=5$ and $x=6$ is . . . . . . sq. units.

Let $g(x) = \cos(x^2)$,$f(x) = \sqrt{x}$,and $\alpha, \beta$ (where $\alpha < \beta$) be the roots of the quadratic equation $18x^2 - 9\pi x + \pi^2 = 0$. Then,the area (in sq. units) bounded by the curve $y = (g \circ f)(x)$ and the lines $x = \alpha$,$x = \beta$,and $y = 0$ is: