The area (in sq. units) of the region

A = {(x, y) : x² $$ \le $$ y $$ \le $$ x + 2} is

Let S($$\alpha $$) = {(x, y) : y² $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ $$\alpha $$} and A($$\alpha $$) is area of the region S($$\alpha $$). If for a $$\lambda $$, 0 < $$\lambda $$ < 4, A($$\lambda $$) : A(4) = 2 : 5, then $$\lambda $$ equals

The area (in sq. units) of the region
A = { (x, y) $$ \in $$ R × R|  0 $$ \le $$ x $$ \le $$ 3, 0 $$ \le $$ y $$ \le $$ 4, y $$ \le $$ x² + 3x} is :

The area (in sq. units) of the region bounded by the parabola, y = x² + 2 and the lines, y = x + 1, x = 0 and x = 3, is