The diagram shows the curve $y = x - 2{\text{ }}ln{\text{ }}x$ and its minimum point $M$.
a) Find the x-coordinate of $M$.
b) Use the trapezium rule with three intervals to estimate the value of
$\int_2^5 {\left( {x - 2ln{\text{ }}x} \right)dx} $,
giving your answer correct to 2 decimal places.
c) 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 (b).

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