4.
\includegraphics[max width=\textwidth, alt={}, center]{fe47eac1-645a-46c6-a2b9-c4ad0bcaa538-1_433_844_1416_575}
The diagram shows the curve with equation \(y = \left( x - \log _ { 10 } x \right) ^ { 2 } , x > 0\).
- Copy and complete the table below for points on the curve, giving the \(y\) values to 2 decimal places.
The shaded region is bounded by the curve, the \(x\)-axis and the lines \(x = 2\) and \(x = 6\).
- Use the trapezium rule with all the values in your table to estimate the area of the shaded region.
- State, with a reason, whether your answer to part (b) is an under-estimate or an over-estimate of the true area.