2024 NCEA Level 3 Integration

2024 Integration AS91579 worked answers

Guided, step-by-step worked solutions for Apply integration methods in solving problems.

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Paper overview

Work through the 2024 questions one step at a time

This page contains 15 independent worked question walkthroughs for NCEA Level 3 Integration (AS91579). Each walkthrough offers hints, reveals the full working in a logical sequence, and focuses on the method described below.

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Worked question index

2024 Integration questions

Choose a question part to open its guided worked solution.

Question 1

Question 1 walkthroughs

Question 1(a) worked solution Recognising a reverse sec-tan derivative pattern. Question 1(b) worked solution Setting up and evaluating a shaded polynomial area. Question 1(c) worked solution Integrating velocity and using a position condition. Question 1(d) worked solution Product-to-sum before integrating a differential equation. Question 1(e) worked solution Finding area between sec² and tan² curves.

Question 2

Question 2 walkthroughs

Question 2(a) worked solution Expanding a square before integrating term by term. Question 2(b) worked solution Solving for a lower limit from a definite integral. Question 2(c) worked solution Separating variables with an exponential model. Question 2(d) worked solution Using trig identities in a shaded \(\sin^2x\) area. Question 2(e) worked solution Logarithmic substitution in a spherical mass model.

Question 3

Question 3 walkthroughs

Question 3(a) worked solution Integrating exponential terms with different inside coefficients. Question 3(b) worked solution Solving a logarithmic differential equation using a condition. Question 3(c) worked solution Decomposing a rational integrand before solving for a parameter. Question 3(d) worked solution Splitting a cosine area into two equal parts. Question 3(e) worked solution Building and solving a Newton's law of cooling model.

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Antidifferentiation Integration techniques Differential equations

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