1.
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\caption{Figure 1}
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Figure 1 shows part of the curve with equation \(y = \mathrm { e } ^ { 0.5 x ^ { 2 } }\). The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis, the \(y\)-axis and the line \(x = 2\).
- Complete the table with the values of \(y\) corresponding to \(x = 0.8\) and \(x = 1.6\).
| \(x\) | 0 | 0.4 | 0.8 | 1.2 | 1.6 | 2 |
| \(y\) | \(\mathrm { e } ^ { 0 }\) | \(\mathrm { e } ^ { 0.08 }\) | | \(\mathrm { e } ^ { 0.72 }\) | | \(\mathrm { e } ^ { 2 }\) |
- Use the trapezium rule with all the values in the table to find an approximate value for the area of \(R\), giving your answer to 4 significant figures.