The area (in sq. units) of the region $A=\{(x, y) : |x|+|y| \leq 1, 2y^{2} \geq |x|\}$ is

The area enclosed between the curves $y^2 = x$ and $y = |x|$ is

If the area of the region ${(x, y) : -2x + 1 \le y \le 4 - x^2, x \ge 0, y \ge 0}$ is $\frac{\alpha}{\beta}$, where $\alpha, \beta \in N$ and $\gcd(\alpha, \beta) = 1$, then the value of $(\alpha + \beta)$ is:

The area (in square units) in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=3$,is

The area of the region enclosed between the circles $x^{2}+y^{2}=4$ and $x^{2}+(y-2)^{2}=4$ is:

Let $T$ be the tangent to the ellipse $E: x^{2}+4 y^{2}=5$ at the point $P(1,1)$. If the area of the region bounded by the tangent $T$,ellipse $E$,lines $x=1$ and $x=\sqrt{5}$ is $\alpha \sqrt{5}+\beta+\gamma \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)$,then $|\alpha+\beta+\gamma|$ is equal to $....$