Explanation

(a)
$Required\ area\ OABO = \int_{0}^{9}{\sqrt{x}\ dx - \int_{3}^{9}\left( \frac{x - 3}{2} \right)dx}$
$= \left( \frac{x^{3/2}}{3/2} \right)_{0}^{9} - \frac{1}{2}\left( \frac{x^{2}}{2} - 3x \right)_{3}^{9}$
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$= \left( \frac{2}{3} \bullet 27 \right) - \frac{1}{2}\left\{ \left( \frac{81}{2} - 27 \right) - \left( \frac{9}{2} - 9 \right) \right\}$
$= 9\ sq\ units$