7 The diagram shows a sketch of two curves.
\includegraphics[max width=\textwidth, alt={}, center]{24641e66-b73b-4323-98c8-349727151aba-14_448_527_370_762} The equations of the two curves are \(y = 1 + \sqrt { x }\) and \(y = 4 ^ { \frac { x } { 9 } }\).
The curves meet at the points \(P ( 0,1 )\) and \(Q ( 9,4 )\).

1. 1. Describe the geometrical transformation that maps the graph of \(y = \sqrt { x }\) onto the graph of \(y = 1 + \sqrt { x }\).
   2. Describe the geometrical transformation that maps the graph of \(y = 4 ^ { x }\) onto the graph of \(y = 4 ^ { \frac { x } { 9 } }\).
2. 1. Given that \(\int _ { 0 } ^ { 9 } \sqrt { x } \mathrm {~d} x = 18\), find the value of \(\int _ { 0 } ^ { 9 } ( 1 + \sqrt { x } ) \mathrm { d } x\).
   2. Use the trapezium rule with five ordinates (four strips) to find an approximate value for \(\int _ { 0 } ^ { 9 } 4 ^ { \frac { x } { 9 } } \mathrm {~d} x\). Give your answer to one decimal place.
   3. Hence find an approximate value for the area of the shaded region bounded by the two curves and state, with an explanation, whether your approximation will be an overestimate or an underestimate of the true value for the area of the shaded region.
      [0pt] [3 marks]