14 The region bounded by the curve
$$y = ( 2 x - 8 ) \ln x$$
and the \(x\)-axis is shaded in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{22ff390e-1360-43bd-8c7f-3d2b58627e91-26_867_908_543_566}
14
- Use the trapezium rule with 5 ordinates to find an estimate for the area of the shaded region.
Give your answer correct to three significant figures.
14 - Show that the exact area is given by
$$32 \ln 2 - \frac { 33 } { 2 }$$
Fully justify your answer.