7 It is given that \(\int _ { 0 } ^ { a } \left( \frac { 4 } { 2 x + 1 } + 8 x \right) \mathrm { d } x = 10\), where \(a\) is a positive constant.
- Show that \(a = \sqrt { 2.5 - 0.5 \ln ( 2 a + 1 ) }\).
- Using the equation in part (a), show by calculation that \(1 < a < 2\).
- Use an iterative formula, based on the equation in part (a), to find the value of \(a\) correct to 4 significant figures. Give the result of each iteration to 6 significant figures.