The area of the region bounded by the curves $x=y^2-2$ and $x=y$ is

Let $f(x) = \max \{\sin^{-1}x, \cos^{-1}x\}$. Then,the area bounded by $x = -1$,$x = 1$,$y = f(x)$,and $y = 0$ is:

The area of the region $\{(x, y): xy \leq 8, 1 \leq y \leq x^2\}$ is

The positive values of the parameter $a$ for which the area of the figure bounded by the curve $y = \cos ax$,$y = 0$,$x = \frac{\pi}{6a}$,and $x = \frac{5\pi}{6a}$ is greater than $3$ are:

The sine and cosine curves intersect infinitely many times,creating bounded regions of equal areas. The area of one such region is

Let the functions $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by $f(x)=e^{x-1}-e^{-|x-1|}$ and $g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right)$. Then the area of the region in the first quadrant bounded by the curves $y=f(x)$,$y=g(x)$ and $x=0$ is