The area (in sq. units) of the region bounded by the curves $y=4|\cos x|$ and $y=-|\cos x|$ from $x=-\frac{\pi}{2}$ to $x=\frac{\pi}{2}$ is

The area of the region bounded by the curves $y=x^{3}$, $y=\frac{1}{x}$, and the line $x=2$ in the first quadrant is:

The area (in square units) of the region bounded by the curves $y + 2x^2 = 0$ and $y + 3x^2 = 1$ is equal to

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

If the area of the region $S=\{(x, y): 2y - y^2 \leq x^2 \leq 2y, x \geq y\}$ is equal to $\frac{n+2}{n+1} - \frac{\pi}{n-1}$,then the natural number $n$ is equal to $...............$.

Find the area bounded on the left by the $y-$axis,below by the $x-$axis,on the right by $x = \frac{\pi}{2}$,above on the left by $y = \cos x$,and above on the right by $y = \sin x$.