Level 3 Integration Walkthrough
2019 NCEA Level 3 Integration Question 2(e)
2019 Paper
Question
The diagram shows the graphs of \(y=(e^x)^2\) and \(y=20-(e^x)^2\). The region between the two curves, from the \(y\)-axis to their intersection, is shaded.
Find the area of the region shaded in the diagram.
You must use calculus and show the results of any integration needed to solve the problem.
First walkthrough idea
Focus to try first
Find the intersection of the two curves, then integrate upper curve minus lower curve from the \(y\)-axis to that point.
Step 1
Find the intersection
The two curves meet where their \(y\)-values are equal.
Show the first step’s working
Walkthrough overview
What this question practises
This 2019 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Finding area between two exponential curves.
This is Question 2(e) 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.
Page updated .
Learning summary
Review the method, not only the answer
This walkthrough helps you practise finding area between two exponential curves. 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.