Level 3 Integration Walkthrough
2019 NCEA Level 3 Integration Question 1(b)
2019 Paper
Question
Use the values given in the table to find an approximation to \(\int_2^5 f(x)\,dx\), using the Trapezium Rule.
| \(x\) | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 |
|---|---|---|---|---|---|---|---|
| \(f(x)\) | 0.6 | 1.1 | 1.7 | 2.6 | 3.2 | 3.4 | 2.6 |
First walkthrough idea
Focus to try first
The \(x\)-values are evenly spaced, so use the Trapezium Rule with width \(h=0.5\).
Step 1
Identify the width
The spacing from \(2\) to \(2.5\), \(2.5\) to \(3\), and so on is \(0.5\).
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: Applying the Trapezium Rule to tabulated values.
This is Question 1(b) 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.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise applying the Trapezium Rule to tabulated values. 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.
Continue practising
- All 2019 Integration walkthroughs
- All AS91579 Integration years
- Practise more questions using this skill: Integration techniques