The area bounded by the curves $y = (x + 1)^2$,$y = (x - 1)^2$ and the line $y = 0$ is

$A$ line passing through the point $A(-2, 0)$ touches the parabola $P: y^2 = x - 2$ at the point $B$ in the first quadrant. The area of the region bounded by the line $AB$,the parabola $P$,and the $x$-axis is:

Let $A_{1}=\{(x, y):|x| \leq y^{2},|x|+2 y \leq 8\}$ and $A_{2}=\{(x, y):|x|+|y| \leq k\}$. If $27 \times \text{Area}(A_{1}) = 5 \times \text{Area}(A_{2})$,then $k$ is equal to

The area bounded between the parabola $y^2 = 4x$ and the line $2x + y - 4 = 0$ 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 area included between the parabolas $y^{2} = 5x$ and $x^{2} = 5y$ is