1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e6b490c0-80c4-4e15-b587-ac052ee27db7-02_738_1257_274_340}
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\caption{Figure 1}
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Figure 1 shows a sketch of part of the curve with equation \(y = \sqrt { } \left( x ^ { 2 } + 1 \right) , x \geqslant 0\)
The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = 2\)
The table below shows corresponding values for \(x\) and \(y\) for \(y = \sqrt { } \left( x ^ { 2 } + 1 \right)\).
| \(x\) | 1 | 1.25 | 1.5 | 1.75 | 2 |
| \(y\) | 1.414 | | 1.803 | 2.016 | 2.236 |
- Complete the table above, giving the missing value of \(y\) to 3 decimal places.
- Use the trapezium rule, with all the values of \(y\) in the completed table, to find an approximate value for the area of \(R\), giving your answer to 2 decimal places.