Level 3 Integration Walkthrough

2024 NCEA Level 3 Integration Question 3(a)

2024 Paper

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Question

\[ \text{Find } \int \left(e^{2x}+\frac{3}{e^{4x}}\right)\,dx. \]

First walkthrough idea

Hint to try first

Rewrite \(\frac{3}{e^{4x}}\) as \(3e^{-4x}\) before integrating.

Step 1

Rewrite the integrand

This makes the power of \(e\) easy to integrate.

Show the first step’s working

This makes the power of \(e\) easy to integrate.

Key result

\[ \frac{3}{e^{4x}}=3e^{-4x} \]

Walkthrough overview

What this question practises

This 2024 walkthrough is part of AS91579 — Apply integration methods in solving problems.

Method: Integrating exponential terms with different inside coefficients.

This is Question 3(a) from the 2024 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 integrating exponential terms with different inside coefficients. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Check the antiderivative by differentiating it, and handle constants and bounds explicitly.

Continue practising

← Question 2(e) Question 3(b) →