Let the area enclosed between the curves $|y|=1-x^2$ and $x^2+y^2=1$ be $\alpha$. If $9\alpha=\beta\pi+\gamma$,where $\beta$ and $\gamma$ are integers,then the value of $|\beta-\gamma|$ equals

The area bounded by the curve $y = x^2 + 1$ and the tangents to it drawn from the origin is

The area enclosed between the curves $y^2 = 4x$ and $y = |x|$ is

Let $A = \{(x, y) : y^2 \le 4x, y - 2x \ge -4\}$. The area of the region $A$ is

The area (in sq. units) of the region bounded by the curves $y = x \log x$ and $y = 2x - 2x^2$ 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