5 It is given that \(a\) is a positive constant such that
$$\int _ { 0 } ^ { a } \left( 1 + 2 x + 3 \mathrm { e } ^ { 3 x } \right) \mathrm { d } x = 250$$
- Show that \(a = \frac { 1 } { 3 } \ln \left( 251 - a - a ^ { 2 } \right)\).
- Use an iterative formula based on the equation in part (i) to find the value of \(a\) correct to 4 significant figures. Give the result of each iteration to 6 significant figures.