Area Under the Curves

The area bounded by the curves $y=\left|x^{2}-1\right|$ and $y=1$ is

The area of the smaller region enclosed by the curves $y^{2}=8 x+4$ and $x^{2}+y^{2}+4 \sqrt{3} x-4=0$ is equal to

The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$, is equal to :

The area of the region enclosed by the curve $f(x)=\max \{\sin x, \cos x\},-\pi \leq x \leq \pi$ and the $x$-axis is

The area enclosed by the curves $y=\log _{e}\left(x+\mathrm{e}^{2}\right), x=\log _{e}\left(\frac{2}{y}\right)$ and $x=\log _{\mathrm{e}} 2$, above the line $y=1$ is:

The area of the region $\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

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

Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x^2-p x+\frac{5}{4} p=0$ are rational. Then the area of the region $\left\{(x, y): 0 \leq y \leq(x-q)^2, 0 \leq x \leq q\right\}$ is :

The area enclosed by the curves $x y+4 y=16$ and $x+y=6$ is equal to :

The area of the region $A = \left\{ {(x,y):\left| {\cos x - \sin x} \right| \le y \le \sin x,0 \le x \le {\pi \over 2}} \right\}$ is