Level 3 Integration Walkthrough
2022 NCEA Level 3 Integration Question 2(b)
2022 Paper
Question
You must use calculus and show the results of any integration needed to solve the problem.
First walkthrough idea
Focus to try first
Turn the radical into a negative power, evaluate the definite integral, then solve the resulting equation for \(k\).
Step 1
Rewrite the integrand
The power rule is easiest to use when the square root is written as an exponent.
Show the first step’s working
Walkthrough overview
What this question practises
This 2022 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Solving for an upper limit from a definite integral.
This is Question 2(b) from the 2022 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.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise solving for an upper limit from a definite integral. 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.