The area (in sq.units) of the region bounded by the curves y = 2^x and y = |x + 1|, in the first quadrant is :

The area (in sq. units) of the region
A = {(x, y) : $${{y{}^2} \over 2}$$ $$ \le $$ x $$ \le $$ y + 4} is :-

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