Integral Calculus
Antidifferentiation, indefinite and definite integrals, the fundamental theorem of calculus, area under and between curves, the trapezoidal rule, and further integration techniques.
Active lessons
16
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
Unit pathway
Lesson pathway
15 of 15 active
Lesson 1
Antidifferentiation and the Reverse Power Rule
Learn integration as the reverse process of differentiation and use the reverse power rule for polynomial terms.
Lesson 2
Indefinite Integrals and the Constant of Integration
Learn why indefinite integrals need a constant of integration and practise integrating polynomial expressions term-by-term.
Lesson 3
Initial Conditions and Finding the Particular Primitive
Use an initial condition or point on a curve to find the value of C and write the particular primitive.
Lesson 4
Definite Integrals and the Fundamental Theorem of Calculus
Evaluate definite integrals using antiderivatives and the Fundamental Theorem of Calculus.
Lesson 5
Signed Area and Total Area
Distinguish between signed area from a definite integral and total geometric area, especially when a graph crosses the x-axis.
Lesson 6
Area Under a Curve
Use definite integrals to find area under a curve, including positive, below-axis, and split-interval cases.
Lesson 7
The Trapezoidal Rule and Area Approximation
Approximate area under a curve using the Trapezoidal rule with table values or evenly spaced function values.
Lesson 8
Area Between Two Curves
Find areas enclosed between two curves by integrating top function minus bottom function.
Lesson 9
Applications of Integration: Total Change and Motion
Use definite integrals to calculate total change, displacement, and contextual quantities from rates.
Lesson 10
Mixed Integral Calculus Exam Practice
Practise mixed HSC-style integration questions involving primitives, definite integrals, area, approximation, and applications.
Lesson 11
Standard Integrals: Trigonometric, Exponential and Logarithmic Forms
Use standard antiderivatives for sine, cosine, exponential and reciprocal functions, including constants of integration.
Lesson 12
Reverse Chain Rule and Simple Substitution Forms
Recognise simple composite integrals where the inner derivative changes the coefficient of the antiderivative.
Lesson 13
Definite Integrals with Standard Forms
Evaluate definite integrals involving trigonometric, exponential and logarithmic standard forms at clean limits.
Lesson 14
Area Between Curves
Find and interpret area between curves using top minus bottom, intersections and interval splitting where needed.
Lesson 15
Further Integral Calculus Exam Practice
Practise mixed HSC-style integration questions involving standard forms, reverse chain rule, definite integrals and area between curves.