If the line y = mx bisects the area enclosed by the lines x = 0, y = 0, x = $${3 \over 2}$$ and the curve y = 1 + 4x $$-$$ x², then 12 m is equal to _____________.

Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x³ $$-$$ 3x² $$-$$ 12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4A is equal to ______________.

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 _______________.