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

29 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

Integration of Inverse Sine Function

Integration of Inverse Cosine Function

Integrations Resulted Inverse Tangent Functions

INTEGRATION OF INVERSE TRIGONOMETRIC FUNCTIONS

APPLICATION OF INTEGRATION

Area Under a Curve

Area between Two Functions

Kinematics using Integration

Volumes using Integration

Volumes for Two Functions

DIFFERENTIAL EQUATIONS

First Order Differential Equations

Slope Fields or Direction Field

Euler's Method of Numerical Integration

Separable Differential Equations