Level 3 Integration Walkthrough

2022 NCEA Level 3 Integration Question 3(b)

2022 Paper

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Question

Use the values in the table below to find an approximation to \(\int_{0}^{2} f(x)\,dx\) using the Trapezium Rule.

\(x\) 0 0.4 0.8 1.2 1.6 2.0
\(f(x)\) 3.6 4.2 4.8 5.4 4.5 3.2

First walkthrough idea

Focus to try first

Identify the common width first, then apply the trapezium rule with endpoints counted once and the middle values counted twice.

Step 1

Identify the strip width

The \(x\)-values increase by a constant amount, so that spacing is the trapezium width \(h\).

Show the first step’s working
\[ h=0.4 \]

Walkthrough overview

What this question practises

This 2022 walkthrough is part of AS91579 — Apply integration methods in solving problems.

Method: Applying the Trapezium Rule from tabulated values.

This is Question 3(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.

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 applying the Trapezium Rule from 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

← Question 3(a) Question 3(c) →