OCR C2 — Question 4

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

4.
\includegraphics[max width=\textwidth, alt={}, center]{fe47eac1-645a-46c6-a2b9-c4ad0bcaa538-1_433_844_1416_575} The diagram 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 region 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.