Paper 3 May/June 2011 MATHEMATICS (9709/31) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

It is given that $\int_1^\alpha {x{\text{ }}ln{\text{ }}x{\text{ }}dx = 22} $, where $\alpha $ is a constant greater than 1.
a) Show that $\alpha = \sqrt {\left( {\frac{{87}}{{2{\text{ }}ln{\text{ }}\alpha - 1}}} \right)} $.
b) Use an iterative formula based on the equation in part (a) to find the value of $\alpha $ correct to 2 decimal places. Use an initial value of 6 and give the result of each iteration to 4 decimal places.