Let $g ( x ) = \cos x ^ { 2 } , f ( x ) = \sqrt { x }$, and $\alpha , \beta ( \alpha < \beta )$ be the roots of the quadratic equation $18 x ^ { 2 } - 9 \pi x + \pi ^ { 2 } = 0$. Then the area (in sq. units) bounded by the curve $y = ( g o f ) ( x )$ and the lines $x = \alpha , x = \beta$ and $y = 0$, is\\
(1) $\frac { 1 } { 2 } ( \sqrt { 2 } - 1 )$\\
(2) $\frac { 1 } { 2 } ( \sqrt { 3 } - 1 )$\\
(3) $\frac { 1 } { 2 } ( \sqrt { 3 } + 1 )$\\
(4) $\frac { 1 } { 2 } ( \sqrt { 3 } - \sqrt { 2 } )$