The area of the region $$S = \{ (x,y):3{x^2} \le 4y \le 6x + 24\} $$ is ____________.

The area (in sq. units) of the region bounded by the curves x² + 2y $$-$$ 1 = 0, y² + 4x $$-$$ 4 = 0 and y² $$-$$ 4x $$-$$ 4 = 0, in the upper half plane is _______________.

Let T be the tangent to the ellipse E : x² + 4y² = 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$$\left( {{1 \over {\sqrt 5 }}} \right)$$, then |$$\alpha$$ + $$\beta$$ + $$\gamma$$| is equal to ______________.

Let f : [$$-$$3, 1] $$ \to $$ R be given as

$$f(x) = \left\{ \matrix{ \min \,\{ (x + 6),{x^2}\}, - 3 \le x \le 0 \hfill \cr \max \,\{ \sqrt x ,{x^2}\} ,\,0 \le x \le 1. \hfill \cr} \right.$$

If the area bounded by y = f(x) and x-axis is A, then the value of 6A is equal to ___________.