Question 1 - A-Level Maths

Exam Board	SPS
Module	SPS SM Pure (SPS SM Pure)
Year	2022
Session	June
Marks	6
Topic	Binomial Theorem (positive integer n)
Type	Direct binomial expansion then integrate

The expression $\left( 2 + x ^ { 2 } \right) ^ { 3 }$ can be written in the form $$8 + p x ^ { 2 } + q x ^ { 4 } + x ^ { 6 }$$ Demonstrate clearly, using the binomial expansion, that $p = 12$ and find the value of $q$.
[0pt] [3 marks]
Hence find $\int \frac { \left( 2 + x ^ { 2 } \right) ^ { 3 } } { x ^ { 4 } } \mathrm {~d} x$.
[0pt] [3 marks]
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