Explanation

(a)
Required area $= \int_{0}^{9}{\sqrt{x}dx - \int_{3}^{9}{\left( \frac{x - 3}{2} \right)dx}}$
$= \left( \frac{x^{3/2}}{3/2} \right)_{0}^{9} - \frac{1}{2}\left( \frac{x^{2}}{2} - 3x \right)_{3}^{9}$
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$= \left( \frac{2}{7} \bullet 27 \right) - \frac{1}{2}\left\{ \left( \frac{81}{2} - 27 \right) - \left( \frac{9}{2} - 9 \right) \right\}$
$= 18 - 9 = 9\ sq\ unit$