2019 NCEA Level 3 Integration

2019 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 2019 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

2019 Integration questions

Choose a question part to open its guided worked solution.

Question 1

Question 1 walkthroughs

Question 1(a) worked solution Rewriting a radical denominator and integrating a power. Question 1(b) worked solution Applying the Trapezium Rule to tabulated values. Question 1(c) worked solution Using product-to-sum before evaluating a trig integral. Question 1(d) worked solution Proving equal areas under a reciprocal-root curve. Question 1(e) worked solution Proving an exponential-growth relation from a differential equation.

Question 2

Question 2 walkthroughs

Question 2(a) worked solution Reversing the chain rule for an exponential term. Question 2(b) worked solution Using signed areas and symmetry on a graph. Question 2(c) worked solution Solving for an upper limit from a logarithmic integral. Question 2(d) worked solution Using the \(\cos^2x\) identity to find shaded area. Question 2(e) worked solution Finding area between two exponential curves.

Question 3

Question 3 walkthroughs

Question 3(a) worked solution Reverse chain rule integration of a cubic power. Question 3(b) worked solution Integrating a \(\sec^2(2x)\) differential equation. Question 3(c) worked solution Rewriting a rational integrand before evaluating it. Question 3(d) worked solution Integrating a derivative and using an initial condition. Question 3(e) worked solution Pumping energy with similar triangles and a definite integral.

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