(i) Use integration by parts to obtain:

\(axe^{-\frac{1}{2}x} + \int be^{-\frac{1}{2}x} \, dx\)

Obtain \(-8xe^{-\frac{1}{2}x} + 8 \int e^{-\frac{1}{2}x} \, dx\)

Obtain \(-8xe^{-\frac{1}{2}x} - 16e^{-\frac{1}{2}x}\)

Use limits correctly and equate to 9:

\(p = 2 \ln \left( \frac{8p + 16}{7} \right)\)

(ii) Use correct iteration formula:

Starting with \(p_0 = 3.5\), iterate:

\(p_1 = 3.6766\)

\(p_2 = 3.7398\)

\(p_3 = 3.7619\)

\(p_4 = 3.7696\)

\(p_5 = 3.7723\)

Final answer: \(p = 3.77\)