Level 3 Integration Walkthrough
2021 NCEA Level 3 Integration Question 2(d)
2021 Integration
Question
The diagram below shows part of the graph of the function
The area of the shaded region is \(4\). Find the value of \(k\).
You must use calculus and show the results of any integration needed to solve the problem.
The diagram is shown in its initial state. JavaScript adds any interactive controls and later walkthrough visuals.
First walkthrough idea
Focus to try first
The shaded area is under \(g(x)=\frac{6}{3x-4}\) from \(x=2\) to \(x=k\). Set that integral equal to \(4\).
Step 1
Set up the area equation
The curve is above the \(x\)-axis on the shaded interval.
Show the first step’s working
Walkthrough overview
What this question practises
This 2021 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Setting a shaded logarithmic area equal to \(4\) and solving for \(k\).
This is Question 2(d) from the 2021 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 setting a shaded logarithmic area equal to \(4\) and solving for \(k\). 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.