4
\includegraphics[max width=\textwidth, alt={}, center]{e429080f-8634-46bc-b451-7b13b871e518-2_543_857_1155_644}
The diagram shows the curve \(\mathrm { y } = \sqrt { 4 \mathrm { X } + 1 }\).
- Use the trapezium rule, with strips of width 0.5 , to find an approximate value for the area of the region bounded by the curve \(y = \sqrt { 4 x + 1 }\), the \(x\)-axis, and the lines \(x = 1\) and \(x = 3\). Give your answer correct to 3 significant figures.
- State with a reason whether this approximation is an under-estimate or an over-estimate.