1.
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\caption{Figure 1}
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Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\)
The table below shows some corresponding values of \(x\) and \(y\) for this curve.
The values of \(y\) are given to 3 decimal places.
| \(x\) | - 1 | - 0.5 | 0 | 0.5 | 1 |
| \(y\) | 2.287 | 4.470 | 6.719 | 7.291 | 2.834 |
Using the trapezium rule with all the values of \(y\) in the given table,
- obtain an estimate for
$$\int _ { - 1 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x$$
giving your answer to 2 decimal places.
- Use your answer to part (a) to estimate
- \(\int _ { - 1 } ^ { 1 } ( \mathrm { f } ( x ) - 2 ) \mathrm { d } x\)
- \(\int _ { 1 } ^ { 3 } \mathrm { f } ( x - 2 ) \mathrm { d } x\)