9 A curve has equation
$$y = x - a \sqrt { x } + b$$
where \(a\) and \(b\) are constants.
The curve intersects the line \(y = 2\) at points with coordinates \(( 1,2 )\) and \(( 9,2 )\), as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{f5e0d980-4c50-4735-aea7-1bdf448a58f7-12_696_807_641_605}
9
- Show that \(a\) has the value 4 and find the value of \(b\)
9 - On the diagram, the region enclosed between the curve and the line \(y = 2\) is shaded.
Show that the area of this shaded region is \(\frac { 16 } { 3 }\)
Fully justify your answer.
[0pt]
[6 marks]