3
\includegraphics[max width=\textwidth, alt={}, center]{322eb555-d40a-460c-8c71-5780f5772bcd-2_535_1041_573_552}
The diagram shows the curve \(y = x - 2 \ln x\) and its minimum point \(M\).
- Find the \(x\)-coordinate of \(M\).
- Use the trapezium rule with three intervals to estimate the value of
$$\int _ { 2 } ^ { 5 } ( x - 2 \ln x ) \mathrm { d } x$$
giving your answer correct to 2 decimal places.
- State, with a reason, whether the trapezium rule gives an under-estimate or an over-estimate of the true value of the integral in part (ii).