Edexcel C2 2014 June — Question 3

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2014
SessionJune
TopicArea Under & Between Curves

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f07cc9ed-a820-46c8-a3a3-3c780cf20fa7-05_821_1273_118_338} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of part of the curve with equation \(y = \sqrt { } ( 2 x - 1 ) , x \geqslant 0.5\) The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the lines with equations \(x = 2\) and \(x = 10\). The table below shows corresponding values of \(x\) and \(y\) for \(y = \sqrt { } ( 2 x - 1 )\).
\(x\)246810
\(y\)\(\sqrt { } 3\)\(\sqrt { } 11\)\(\sqrt { } 19\)
  1. Complete the table with the values of \(y\) corresponding to \(x = 4\) and \(x = 8\).
  2. Use the trapezium rule, with all the values of \(y\) in the completed table, to find an approximate value for the area of \(R\), giving your answer to 2 decimal places.
  3. State whether your approximate value in part (b) is an overestimate or an underestimate for the area of \(R\).