Level 3 Integration Walkthrough

2021 NCEA Level 3 Integration Question 3(b)

2021 Integration

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Question

Use the values given in the table below to find an approximation to \(\int_{1}^{2.5}f(x)\,dx\) using the Trapezium Rule.

\(x\) 1 1.25 1.5 1.75 2 2.25 2.5
\(f(x)\) 0.8 1.1 1.5 1.9 2.2 2.1 2.4

First walkthrough idea

Focus to try first

The \(x\)-values are evenly spaced by \(0.25\), so use that as the trapezium width.

Step 1

Find the width

The gap between consecutive \(x\)-values is constant.

Show the first step’s working
\[ h=1.25-1=0.25 \]

Walkthrough overview

What this question practises

This 2021 walkthrough is part of AS91579 — Apply integration methods in solving problems.

Method: Applying the Trapezium Rule with a width of \(0.25\).

This is Question 3(b) from the 2021 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 with a width of \(0.25\). 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) →