Course: Year 12 Mathematics Advanced

Integral Calculus

A staged pathway through integration skills, starting with antidifferentiation and building toward definite integrals, area, applications, and mixed exam practice.

Active lessons

10

Planned lessons

10

Lesson sequence

Learn -> Guided Practice -> Independent Practice -> Mastery Quiz

How to use this unit

  • Start with antidifferentiation before moving to indefinite integrals.
  • Use the mastery quiz to check whether the idea is secure.
  • If you miss the pass mark, work through the full staged lesson.
  • Return to earlier lessons when later area questions feel shaky.

What this unit covers

Antidifferentiation
Indefinite integrals and + C
Initial conditions
Definite integrals
Fundamental Theorem of Calculus
Signed area and total area
Area under a curve
Trapezoidal rule
Area between curves
Total change and motion applications
Mixed exam practice

Unit pathway

Lesson pathway

10 of 10 active

1

Lesson 1

Antidifferentiation and the reverse power rule

Understand integration as reverse differentiation and use the reverse power rule.

Active
2

Lesson 2

Indefinite integrals and the constant of integration

Use +C and integrate polynomial expressions term-by-term.

Active
3

Lesson 3

Initial conditions and finding the particular primitive

Use a point or condition to find the value of C in an indefinite integral.

Active
4

Lesson 4

Definite integrals and the Fundamental Theorem of Calculus

Evaluate definite integrals using antiderivatives and understand what the bounds mean.

Active
5

Lesson 5

Signed area and total area

Distinguish between signed area from a definite integral and total geometric area.

Active
6

Lesson 6

Area under a curve

Use definite integrals to calculate areas bounded by curves and the x-axis.

Active
7

Lesson 7

The Trapezoidal rule and area approximation

Approximate area under a curve using the Trapezoidal rule.

Active
8

Lesson 8

Area between two curves

Find areas enclosed between two curves by integrating the difference between functions.

Active
9

Lesson 9

Applications of integration: total change and motion

Use integration to calculate total change, displacement, and other contextual quantities from rates.

Active
10

Part of the Online Learning Package

This unit is part of the Nova Maths online learning package. The lesson pathway is available for preview, and full access requires an active online learning subscription.

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