The area bounded by the curve $y = x|x|$,$X$-axis and the ordinates $x = -1$ and $x = 1$ is . . . . . . .

The area (in $sq. \,units$) of the region,given by the set $\{(x, y) \in R \times R \mid x \geq 0, 2x^2 \leq y \leq 4-2x\}$ is:

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:

The area of the region bounded by the curve $y = \cos x$,the $X$-axis,and the lines $x = 0$ and $x = \pi$ is . . . . . . sq. units.

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

The area of the region bounded by the curve $y = x^2 - x - 6$,the $x$-axis $(y = 0)$,and the lines $x = -1$ and $x = 1$ is . . . . . . sq. units.