9709 P33 - Nov 2013 - Q5
1849
It is given that \(\int_0^p 4xe^{-\frac{1}{2}x} \, dx = 9\), where \(p\) is a positive constant.
(i) Show that \(p = 2 \ln \left( \frac{8p + 16}{7} \right)\).
(ii) Use an iterative process based on the equation in part (i) to find the value of \(p\) correct to 3 significant figures. Use a starting value of 3.5 and give the result of each iteration to 5 significant figures.
