Level 3 Integration Walkthrough
2023 NCEA Level 3 Integration Question 2(d)
2023 Paper
Question
First walkthrough idea
Focus to try first
Differentiate the denominator and then scale it so it matches the numerator.
Step 1
Differentiate the denominator
Both trig terms bring out a factor of \(2\).
Show the first step’s working
Both trig terms bring out a factor of \(2\).
Key result
\[ -2\sin 2x-2\cos 2x \]Walkthrough overview
What this question practises
This 2023 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Spotting a logarithmic quotient by differentiating the denominator.
This is Question 2(d) from the 2023 NCEA Level 3 Integration paper for AS91579 — Apply integration methods in solving problems. Use the guided hints to practise the method before revealing the full working.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise spotting a logarithmic quotient by differentiating the denominator. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Keep logarithm domain restrictions and any inner-function factor visible throughout the working.