Question 3 - A-Level Maths

Exam Board	AQA
Module	C2 (Core Mathematics 2)
Year	2011
Session	June
Topic	Binomial Theorem (positive integer n)
Type	Expansion with algebraic manipulation then integrate

The expression $\left( 2 + x ^ { 2 } \right) ^ { 3 }$ can be written in the form $$8 + p x ^ { 2 } + q x ^ { 4 } + x ^ { 6 }$$ Show that $p = 12$ and find the value of the integer $q$.
1. Hence find $\int \frac { \left( 2 + x ^ { 2 } \right) ^ { 3 } } { x ^ { 4 } } \mathrm {~d} x$.
  (5 marks)
2. Hence find the exact value of $\int _ { 1 } ^ { 2 } \frac { \left( 2 + x ^ { 2 } \right) ^ { 3 } } { x ^ { 4 } } \mathrm {~d} x$.
  (2 marks)