HSC Year 12 Mathematics Extension 1 Calculus
Course

HSC Year 12 Mathematics Extension 1 – Calculus

4.1 Integration
4.2 Differentiation of Inverse Trigonometric Functions
4.3 Integration of Inverse Trigonometric Functions
4.4 Applications of Integration
4.5 Differential Equations

33 Lessons

Course Materials

INTEGRATION

Indefinite Integration by Recognition

Integration by Substitution

Definite Integration by Substitution

Further Integration of Trigonometric Functions by Substitution

Further Integration of Trigonometric Functions using Properties

Integration using Substitution in Right-Angled Triangles

Upper and Lower Rectangles

Definite Integrals

Definite Integration of Power Functions

DIFFERENTIATION OF INVERSE TRIGONOMETRIC FUNCTIONS

Differentiation of Inverse Sine Function

Differentiation of Inverse Cosine Function

Differentiation of Inverse Tangent Function

INTEGRATIONS RESULTING IN INVERSE TRIGONOMETRIC FUNCTIONS

Integrations Resulting in Inverse Sine Functions

Integrations Resulting in Inverse Cosine Functions

Integrations Resulting in Inverse Tangent Functions

APPLICATION OF INTEGRATION

Area Under a Curve

Signed Areas

Area between Two Functions

Area between Two Functions involving Signed Areas

Area under Trigonometric Curves

Kinematics using Integration

Volumes using Integration

Volumes for Two Functions

Volumes using Integration of Trigonometric Functions

DIFFERENTIAL EQUATIONS

Differential Equations of the Form dy/dx = f(x)

Differential Equations of the Form dy/dx = g(y)

Separable Differential Equations

Setting Up Differential Equations