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

The area bounded by the curves $y=(x-1)^2$,$y=(x+1)^2$ and $y=\frac{1}{4}$ is

The area enclosed by the curves $y = \sin^{-1}(\cos x)$ and $y = \cos^{-1}(\sin x)$ for $x \in \left[ \frac{\pi}{2}, \frac{3\pi}{2} \right]$ is:

Let the function $f(x) = \begin{cases} -3ax^2 - 2, & x < 1 \\ a^2 + bx, & x \geq 1 \end{cases}$ be differentiable for all $x \in R$,where $a > 1, b \in R$. If the area of the region enclosed by $y = f(x)$ and the line $y = -20$ is $\alpha + \beta \sqrt{3}$,where $\alpha, \beta \in Z$,then the value of $\alpha + \beta$ is . . . . .

Find the area of the region enclosed between the two circles $:$ $x^{2}+y^{2}=4$ and $(x-2)^{2}+y^{2}=4$.

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