Level 3 Integration Walkthrough
2018 NCEA Level 3 Integration Question 3(c)
2018 Paper
Question
Find the value of \(k\), given that
First walkthrough idea
Focus to try first
Integrate the exponential, evaluate at zero and \(k\), then use logarithms to isolate \(k\).
Step 1
Integrate the exponential
Divide by the inside coefficient \(0.5\).
Show the first step’s working
Walkthrough overview
What this question practises
This 2018 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Solving an exponential definite integral for its limit.
This is Question 3(c) from the 2018 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 solving an exponential definite integral for its limit. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.