Use the mid-ordinate rule with four strips to find an estimate for \(\int _ { 1 } ^ { 5 } \ln x \mathrm {~d} x\), giving your answer to three significant figures.
Given that \(y = x \ln x\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
Hence, or otherwise, find \(\int \ln x \mathrm {~d} x\).
Find the exact value of \(\int _ { 1 } ^ { 5 } \ln x \mathrm {~d} x\).