The area of the region bounded by the curve $y = \cos x$,$-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$ and the $X$-axis is . . . . . . sq. units.

The odd natural number $a$ such that the area of the region bounded by $y = 1, y = 3, x = 0,$ and $x = y^a$ is $\frac{364}{3}$ is equal to:

The area bounded by the lines $y=x$,$x=-1$,$x=2$ and the $X$-axis is

The area (in square units) lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines $x=0$ and $x=2$ is

The graphs of $f(x) = x^2$ and $g(x) = cx^3$ (where $c > 0$) intersect at the points $(0, 0)$ and $\left( \frac{1}{c}, \frac{1}{c^2} \right)$. If the area of the region lying between these graphs over the interval $[0, 1/c]$ is equal to $2/3$,then the value of $c$ is:

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