2017 NCEA Level 3 Integration

2017 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 2017 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

2017 Integration questions

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Question 1

Question 1 walkthroughs

Question 1(a) worked solution Reversing the derivative of a tangent function. Question 1(b) worked solution Using a definite integral to find an enclosed area. Question 1(c) worked solution Building velocity and displacement from acceleration. Question 1(d) worked solution Solving for an unknown limit in an exponential integral. Question 1(e) worked solution Finding a mean value using a squared-trigonometric identity.

Question 2

Question 2 walkthroughs

Question 2(a) worked solution Logarithmic integration with a linear denominator. Question 2(b) worked solution Reversing the chain rule for a linear power. Question 2(c) worked solution Finding the shaded area between a parabola and its tangent. Question 2(d) worked solution Product-to-sum before integrating a trigonometric area. Question 2(e) worked solution Integrating logarithmic acceleration to find velocity.

Question 3

Question 3 walkthroughs

Question 3(a) worked solution Integrating polynomial and exponential terms. Question 3(b) worked solution Applying the Trapezium Rule to courtyard measurements. Question 3(c) worked solution Rewriting a rational function to find the exact courtyard area. Question 3(d) worked solution Solving a separable differential equation with a condition. Question 3(e) worked solution Substitution in a parameterised differential equation.

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