4. \begin{figure}[h] \end{figure} Figure 1 shows a sketch of part of the curve with equation \(y = \frac { x } { 1 + \sqrt { } x }\). The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis, the line with equation \(x = 1\) and the line with equation \(x = 4\).

1. Complete the table with the value of \(y\) corresponding to \(x = 3\), giving your answer to 4 decimal places.
   (1)

   \(x\)	1	2	3	4
   \(y\)	0.5	0.8284		1.3333

2. Use the trapezium rule, with all the values of \(y\) in the completed table, to obtain an estimate of the area of the region \(R\), giving your answer to 3 decimal places.
3. Use the substitution \(u = 1 + \sqrt { } x\), to find, by integrating, the exact area of \(R\).
   \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{a98d4a7f-1e6d-4294-9b5c-c945e8fbe83e-07_743_1568_219_182} \captionsetup{labelformat=empty} \caption{Figure 2}
   \end{figure} Figure 2 shows a sketch of part of the curve \(C\) with parametric equations $$x = 1 - \frac { 1 } { 2 } t , \quad y = 2 ^ { t } - 1$$ The curve crosses the \(y\)-axis at the point \(A\) and crosses the \(x\)-axis at the point \(B\).