Question 4 - A-Level Maths

Exam Board	AQA
Module	C2 (Core Mathematics 2)
Year	2010
Session	June
Topic	Binomial Theorem (positive integer n)
Type	Direct binomial expansion then integrate

The expression $\left( 1 - \frac { 1 } { x ^ { 2 } } \right) ^ { 3 }$ can be written in the form $$1 + \frac { p } { x ^ { 2 } } + \frac { q } { x ^ { 4 } } - \frac { 1 } { x ^ { 6 } }$$ Find the values of the integers $p$ and $q$.
1. Hence find $\int \left( 1 - \frac { 1 } { x ^ { 2 } } \right) ^ { 3 } \mathrm {~d} x$.
2. Hence find the value of $\int _ { \frac { 1 } { 2 } } ^ { 1 } \left( 1 - \frac { 1 } { x ^ { 2 } } \right) ^ { 3 } \mathrm {~d} x$.
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