AQA C2 2008 June — Question 7

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2008
SessionJune
TopicBinomial Theorem (positive integer n)
TypeDirect binomial expansion then integrate

7
  1. The expression \(\left( 1 + \frac { 4 } { x ^ { 2 } } \right) ^ { 3 }\) can be written in the form $$1 + \frac { p } { x ^ { 2 } } + \frac { q } { x ^ { 4 } } + \frac { 64 } { x ^ { 6 } }$$ By using the binomial expansion, or otherwise, find the values of the integers \(p\) and \(q\).
    1. Hence find \(\int \left( 1 + \frac { 4 } { x ^ { 2 } } \right) ^ { 3 } \mathrm {~d} x\).
    2. Hence find the value of \(\int _ { 1 } ^ { 2 } \left( 1 + \frac { 4 } { x ^ { 2 } } \right) ^ { 3 } \mathrm {~d} x\).