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The diagram shows part of the curve \(y = \sqrt { x ^ { 2 } - 1 }\).
- Use the trapezium rule with 4 intervals to find an estimate for \(\int _ { 1 } ^ { 3 } \sqrt { x ^ { 2 } - 1 } \mathrm {~d} x\).
Give your answer correct to \(\mathbf { 3 }\) significant figures.
- State whether the value from part (a) is an under-estimate or an over-estimate, giving a reason for your answer.
- Explain how the trapezium rule could be used to obtain a more accurate estimate.