If the area of the region bounded by the curves, $$y = {x^2},y = {1 \over x}$$ and the lines y = 0 and x= t (t >1) is 1 sq. unit, then t is equal to :

Let g(x) = cosx², f(x) = $$\sqrt x $$ and $$\alpha ,\beta \left( {\alpha < \beta } \right)$$ be the roots of the quadratic equation 18x² - 9$$\pi $$x + $${\pi ^2}$$ = 0. Then the area (in sq. units) bounded by the curve
y = (gof)(x) and the lines $$x = \alpha $$, $$x = \beta $$ and y = 0 is :

The area (in sq. units) of the region

{x $$ \in $$ R : x $$ \ge $$ 0, y $$ \ge $$ 0, y $$ \ge $$ x $$-$$ 2  and y $$ \le $$ $$\sqrt x $$}, is :

The area (in sq. units) of the smaller portion enclosed between the curves, x² + y² = 4 and y² = 3x, is :