Level 3 Integration Walkthrough

2020 NCEA Level 3 Integration Question 2(a)

2020 Paper

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Question

Question 2(a) original exam prompt; text transcription follows

First walkthrough idea

Focus to try first

Rewrite the reciprocal square as \(x^{-2}\), then apply the power rule.

Step 1

Rewrite in exponential form

The negative power makes the sign change in the antiderivative easy to track.

Show the first step’s working
\[ \int\left(\pi-\frac2{x^2}\right)\,dx =\int\left(\pi-2x^{-2}\right)\,dx \]

Walkthrough overview

What this question practises

This 2020 walkthrough is part of AS91579 — Apply integration methods in solving problems.

Method: Integrating a reciprocal-square term.

This is Question 2(a) from the 2020 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 integrating a reciprocal-square term. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Check the antiderivative by differentiating it, and handle constants and bounds explicitly.

Continue practising

← Question 1(e) Question 2(b) →