4. (a) Complete the table below, giving values of \(\sqrt { } \left( 2 ^ { x } + 1 \right)\) to 3 decimal places.
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
| \(\sqrt { } \left( 2 ^ { x } + 1 \right)\) | 1.414 | 1.554 | 1.732 | 1.957 | | | 3 |
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{78a994ba-50c5-434f-a060-9596edb505cd-05_653_595_616_676}
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\caption{Figure 1}
\end{figure}
Figure 1 shows the region \(R\) which is bounded by the curve with equation \(y = \sqrt { } \left( 2 ^ { x } + 1 \right)\), the \(x\)-axis and the lines \(x = 0\) and \(x = 3\)
(b) Use the trapezium rule, with all the values from your table, to find an approximation for the area of \(R\).
(c) By reference to the curve in Figure 1 state, giving a reason, whether your approximation in part (b) is an overestimate or an underestimate for the area of \(R\).