9 The constant \(a\) is such that \(\int _ { 0 } ^ { a } x \mathrm { e } ^ { - 2 x } \mathrm {~d} x = \frac { 1 } { 8 }\).
- Show that \(a = \frac { 1 } { 2 } \ln ( 4 a + 2 )\).
- Verify by calculation that \(a\) lies between 0.5 and 1 .
- Use an iterative formula based on the equation in (a) to determine \(a\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.