In the figure given below,if the areas of the two regions are equal,then which of the following is true?

The area (in sq. units) enclosed between the curves $y=x^2$ and $y=|x|$ is

The area (in sq. units) bounded by the curves $y=\frac{8}{x}$,$y=2x$ and $x=4$ is

The area (in sq. units) of the part of the circle $x^2+y^2=169$ which is below the line $5x-y=13$ is $\frac{\pi \alpha}{2 \beta}-\frac{65}{2}+\frac{\alpha}{\beta} \sin ^{-1}\left(\frac{12}{13}\right)$ where $\alpha, \beta$ are coprime numbers. Then $\alpha+\beta$ is equal to . . . . . . .

The area bounded by the curve $y=\cos x$,the line joining $(-\pi / 4, \cos (-\pi / 4))$ and $(0,2)$ and the line joining $(\pi / 4, \cos (\pi / 4))$ and $(0,2)$ is

The area of the region bounded by the lines $x=1, x=2$,and the curves $x(y-e^x)=\sin x$ and $2xy=2\sin x+x^3$ is