The area of the region described by $\{(x, y) \mid x^2+y^2 \leq 1\}$ and $\{y^2 \leq 1-x\}$ is

The area (in square units) of the region enclosed between the parabola $y^2=2x$ and the line $y=4x-1$ is:

The area (in square units) bounded by the curves $x = -2y^2$ and $x = 1 - 3y^2$ is

Let the area enclosed by the lines $x + y = 2, y = 0, x = 0$ and the curve $f(x) = \min \left\{x^2 + \frac{3}{4}, 1 + [x]\right\}$,where $[x]$ denotes the greatest integer $\leq x$,be $A$. Then the value of $12A$ is $............$.

Let $a$ and $b$ respectively be the points of local maximum and local minimum of the function $f(x)=2 x^{3}-3 x^{2}-12 x$. If $A$ is the total area of the region bounded by $y=f(x)$,the $x$-axis and the lines $x=a$ and $x=b$,then $4 A$ is equal to ..... .

The following figure shows the graph of a continuous function $y=f(x)$ on the interval $[1,3]$. The points $A, B, C$ have coordinates $(1,1), (3,2), (2,3)$ respectively,and the lines $l_1$ and $l_2$ are parallel,with $l_1$ being tangent to the curve at $C$. If the area under the graph of $y=f(x)$ from $x=1$ to $x=3$ is $4$ sq units,then the area of the shaded region is