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

Question

( A ) $\frac{1}{2} (\sqrt{3}+1)$
( B ) $\frac{1}{2} (\sqrt{2}-1)$
( C ) $\frac{1}{2} (\sqrt{3}-1)$
( D ) $\frac{1}{2} (\sqrt{3}-\sqrt{2})$