Use Simpson's rule, with five ordinates (four strips), to calculate an estimate for
$$\int _ { 0 } ^ { 4 } \frac { x } { x ^ { 2 } + 2 } \mathrm {~d} x$$
Give your answer to four significant figures.
Show that the exact value of \(\int _ { 0 } ^ { 4 } \frac { x } { x ^ { 2 } + 2 } \mathrm {~d} x\) is \(\ln k\), where \(k\) is an integer. (5 marks)