If the area bounded by the curve $2y^2 = 3x$,the lines $x+y=3$,$y=0$ and outside the circle $(x-3)^2 + y^2 = 2$ is $A$,then $4(\pi + 4A)$ is equal to $.........$.

Let for $x \in R$; $f(x) = \frac{x+|x|}{2}$ and $g(x) = \begin{cases} x, & x < 0 \\ x^2, & x \geq 0 \end{cases}$. Then the area bounded by the curve $y = (f \circ g)(x)$ and the lines $y = 0$,$2y - x = 15$ is equal to $...........$.

The area bounded by the curves $y=2x^2$,$y=\max \{x-[x], x+|x|\}$ and the lines $x=0, x=2$ (in sq units) is

Let $f :[-3,1] \rightarrow R$ be given as
$f(x)=\begin{cases} \min \{(x+6), x^{2}\}, & -3 \leq x \leq 0 \\ \max \{\sqrt{x}, x^{2}\}, & 0 \leq x \leq 1 \end{cases}$
If the area bounded by $y = f(x)$ and the $x$-axis is $A$,then the value of $6A$ is equal to ....... .

If the area of the region $\{(x, y): 0 \leq y \leq \min \{2x, 6x-x^2\}\}$ is $A$,then $12A$ is equal to

The area of the region bounded by the parabola $(y-2)^{2}=(x-1)$,the tangent to it at the point whose ordinate is $3$,and the $x$-axis is: