The table below shows corresponding values of \(x\) and \(y\) for \(y = \log _ { 3 } 2 x\) The values of \(y\) are given to 2 decimal places as appropriate.
\(x\)
3
4.5
6
7.5
9
\(y\)
1.63
2
2.26
2.46
2.63
Using the trapezium rule with all the values of \(y\) in the table, find an estimate for
$$\int _ { 3 } ^ { 9 } \log _ { 3 } 2 x \mathrm {~d} x$$
Using your answer to part (a) and making your method clear, estimate