JEE Math Practice Question

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 :

1. A.$${1 \over 2}\left( {\sqrt 2 - 1} \right)$$
2. B.$${1 \over 2}\left( {\sqrt 3 - 1} \right)$$
3. C.$${1 \over 2}\left( {\sqrt 3 + 1} \right)$$
4. D.$${1 \over 2}\left( {\sqrt 3 - \sqrt 2 } \right)$$