4 It is given that \(\int _ { a } ^ { 3 a } \left( \mathrm { e } ^ { 3 x } + \mathrm { e } ^ { x } \right) \mathrm { d } x = 100\), where \(a\) is a positive constant.
- Show that \(a = \frac { 1 } { 9 } \ln \left( 300 + 3 \mathrm { e } ^ { a } - 2 \mathrm { e } ^ { 3 a } \right)\).
- Use an iterative process, based on the equation in part (i), to find the value of \(a\) correct to 4 decimal places. Use a starting value of 0.6 and show the result of each step of the process.