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\includegraphics[max width=\textwidth, alt={}, center]{73d67b39-3611-4afb-9470-2f813115abb5-4_415_714_287_678}
The diagram shows the curve \(y = 1.25 ^ { x }\).
- A point on the curve has \(y\)-coordinate 2. Calculate its \(x\)-coordinate.
- Use the trapezium rule with 4 intervals to estimate the area of the shaded region, bounded by the curve, the axes, and the line \(x = 4\).
- State, with a reason, whether the estimate found in part (ii) is an overestimate or an underestimate.
- Explain briefly how the trapezium rule could be used to find a more accurate estimate of the area of the shaded region.