Level 3 Integration Walkthrough
2023 NCEA Level 3 Integration Question 1(c)
2023 Paper
Question
The graph below shows the functions \(y=\sqrt{x}\) and \(8y=x^2\).
Find the shaded area.
The diagram is shown in its initial state. JavaScript adds any interactive controls and later walkthrough visuals.
First walkthrough idea
Focus to try first
Find the intersection points first, then integrate top minus bottom over that interval.
Step 1
Find the non-zero intersection
Solving \(x^3=64\) gives \(x=4\).
Show the first step’s working
Solving \(x^3=64\) gives \(x=4\).
Key result
Walkthrough overview
What this question practises
This 2023 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Finding intersections and the area between \(\sqrt{x}\) and \(\frac{x^2}{8}\).
This is Question 1(c) 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.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise finding intersections and the area between \(\sqrt{x}\) and \(\frac{x^2}{8}\). 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.