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The diagram shows the curve \(y = \frac { \ln x } { x ^ { 2 } }\) and its maximum point \(M\).
- Find the exact coordinates of \(M\).
- Use the trapezium rule with three intervals to estimate the value of
$$\int _ { 1 } ^ { 4 } \frac { \ln x } { x ^ { 2 } } \mathrm {~d} x$$
giving your answer correct to 2 decimal places.