1.
\begin{figure}[h]
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\caption{Figure 1}
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Figure 1 shows a sketch of part of the curve with equation
$$y = \frac { ( x + 2 ) ^ { \frac { 3 } { 2 } } } { 4 } , \quad x \geqslant - 2$$
The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the line with equation \(x = 10\)
The table below shows corresponding values of \(x\) and \(y\) for \(y = \frac { ( x + 2 ) ^ { \frac { 3 } { 2 } } } { 4 }\)
- Complete the table, giving values of \(y\) corresponding to \(x = 2\) and \(x = 6\)
| \(x\) | - 2 | 2 | 6 | 10 |
| \(y\) | 0 | | | \(6 \sqrt { } 3\) |
- Use the trapezium rule, with all the values of \(y\) from the completed table, to find an approximate value for the area of \(R\), giving your answer to 3 decimal places.