If the area (in $sq. units$) of the region $\{(x,y): y^2 \le 4x, x + y \le 1, x \ge 0, y \ge 0\}$ is $a\sqrt{2} + b$,then $a - b$ is equal to

The area (in sq units) bounded by the curves $y^2=4x$ and $x^2=4y$ is

The curve $y = ax^2 + bx + c$ passes through the point $(1, 2)$ and its tangent at the origin is the line $y = x$. The area bounded by the curve,the ordinate of the curve at its minima,and the tangent line is

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

One of the points of intersection of the curves $y=1+3x-2x^2$ and $y=\frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$. Let the area of the region enclosed by these curves be $\frac{1}{24}(\ell \sqrt{5}+m)-n \log_{e}(1+\sqrt{5})$,where $\ell, m, n \in N$. Then $\ell+m+n$ is equal to

The area (in $sq. \, units$) of the region bounded by the curves $x^{2}+2y-1=0$,$y^{2}+4x-4=0$,and $y^{2}-4x-4=0$ in the upper half plane is $....$