Level 3 Integration Walkthrough

2019 NCEA Level 3 Integration Question 3(a)

2019 Paper

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Question

Question 3(a) original exam prompt; text transcription follows

First walkthrough idea

Focus to try first

Use the reverse chain rule on \((2x-1)^3\); the inside derivative is \(2\).

Step 1

Set up the reverse chain rule

Increase the power from \(3\) to \(4\), then divide by both the new power and the inside derivative.

Show the first step’s working
\[ \int24(2x-1)^3\,dx = \frac{24(2x-1)^4}{4\cdot2}+C \]

Walkthrough overview

What this question practises

This 2019 walkthrough is part of AS91579 — Apply integration methods in solving problems.

Method: Reverse chain rule integration of a cubic power.

This is Question 3(a) from the 2019 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.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91579.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise reverse chain rule integration of a cubic power. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Do not stop after differentiating the outside function; include the derivative of the inside function as a factor.

Continue practising

← Question 2(e) Question 3(b) →