Level 3 Integration Walkthrough
2023 NCEA Level 3 Integration Question 1(e)
2023 Paper
Question
The shaded region is bounded by the three graphs
Find the area of the shaded region.
The diagram is shown in its initial state. JavaScript adds any interactive controls and later walkthrough visuals.
First walkthrough idea
Focus to try first
Follow the PDF strategy: find the key intersections, integrate the large curved region first, then subtract the small cap above \(y=3x\).
Step 1
Find the key intersection values
Those are the points where the boundary changes.
Show the first step’s working
Those are the points where the boundary changes.
Key result
\[ x=0,\ 1,\ 10 \]Walkthrough overview
What this question practises
This 2023 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Combining curve intersections with a subtract-a-cap area strategy.
This is Question 1(e) 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.
Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91579.
Page updated .
Learning summary
Review the method, not only the answer
This walkthrough helps you practise combining curve intersections with a subtract-a-cap area strategy. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check intersections, signs, and whether the question asks for signed area or total geometric area.