Level 3 Integration Walkthrough
2020 NCEA Level 3 Integration Question 2(b)
2020 Paper
Question
Use the values given in the table to find an approximation to \(\int_0^3 f(x)\,dx\), using Simpson's Rule.
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
|---|---|---|---|---|---|---|---|
| \(f(x)\) | 1.1 | 1.8 | 2.1 | 2.4 | 2.7 | 1.8 | 1.3 |
First walkthrough idea
Focus to try first
There are six equal strips of width \(h=0.5\), so Simpson’s Rule uses weights \(1,4,2,4,2,4,1\).
Step 1
Find the strip width
Read the constant spacing between consecutive \(x\)-values in the table.
Show the first step’s working
Walkthrough overview
What this question practises
This 2020 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Applying Simpson’s Rule to tabulated values.
This is Question 2(b) from the 2020 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 Simpson’s 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 2020 Integration walkthroughs
- All AS91579 Integration years
- Practise more questions using this skill: Integration techniques