Course: Year 12 Mathematics Advanced

Further Integral Calculus

A HSC-focused unit for standard trigonometric, exponential and logarithmic integrals, reverse chain rule, definite integrals and numerical integration, including the trapezoidal rule and area between curves.

Active lessons

6

Planned lessons

6

Lesson sequence

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

How to use this unit

  • Review standard derivatives before choosing antiderivatives.
  • Use multiple-choice options to compare symbolic forms safely.
  • Check inner derivative factors in reverse-chain questions.
  • Use table values carefully when applying the trapezoidal rule.
  • Use top minus bottom for area between curves.

What this unit covers

Standard trigonometric integrals
Exponential and logarithmic forms
Reverse chain rule
Definite integrals with standard forms
Trapezoidal rule
Area between curves
Mixed HSC-style practice

Unit pathway

Lesson pathway

6 of 6 active

1

Lesson 1

Standard Integrals: Trigonometric, Exponential and Logarithmic Forms

Use standard antiderivatives for sine, cosine, exponential and reciprocal functions, including constants of integration.

Active
2

Lesson 2

Reverse Chain Rule and Simple Substitution Forms

Recognise simple composite integrals where the inner derivative changes the coefficient of the antiderivative.

Active
3

Lesson 3

Definite Integrals with Standard Forms

Evaluate definite integrals involving trigonometric, exponential and logarithmic standard forms at clean limits.

Active
4

Lesson 4

Area Between Curves

Find and interpret area between curves using top minus bottom, intersections and interval splitting where needed.

Active
5

Lesson 5

The Trapezoidal Rule

Approximate definite integrals from functions or tables using one or more trapezoids, and interpret the effect of concavity.

Active
6