Edexcel C2 — Question 6

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

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{857bf144-b03e-4b46-b043-1119b30f9e78-3_572_954_246_497} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the curve with equation \(y = \left( x - \log _ { 10 } x \right) ^ { 2 } , x > 0\).
  1. Copy and complete the table below for points on the curve, giving the \(y\) values to 2 decimal places.
    \(x\)23456
    \(y\)2.896.36
    The shaded area is bounded by the curve, the \(x\)-axis and the lines \(x = 2\) and \(x = 6\).
  2. Use the trapezium rule with all the values in your table to estimate the area of the shaded region.
  3. State, with a reason, whether your answer to part (b) is an under-estimate or an over-estimate of the true area.