## Course curriculum

• 1

### 4.1 Standard Integrals & Completing the Square

• Integration in Extension 2

• Completing the Square

• Example 1

• Example 1 Video

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Example 4

• Example 4 Video

• Exercise 4.1

• Exercise 4.1 Recorded Solutions

• 2

### 4.2 The Reverse Chain Rule and U Substitutions

• The Reverse Chain Rule and U Substitutions

• Example 1

• Example 1 Video

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Example 4

• Example 4 Video

• Example 5

• Example 5 Video

• Exercise 4.2

• Exercise 4.2 Recorded Solutions

• 3

### 4.3 Splitting the Numerator

• Splitting the Numerator

• Example 1

• Example 1 Video

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Splitting the Numerator (Part II)

• Example 4

• Example 4 Video

• Partial Fractions by Inspection

• Example 5

• Example 5 Video

• Example 6

• Example 6 Video

• Exercise 4.3

• Exercise 4.3 Recorded Solutions

• 4

### 4.4 Partial Fractions

• Partial Fractions (Equating Coefficients)

• Example 1

• Example 1 Video

• Partial Fractions (Elimination by Substitution)

• Example 2

• Example 2 Video

• Notes on Substitution Method

• Partial Fractions (Cover Up Method)

• Example 3

• Example 3 Video

• Partial Fractions (Cover Up Method II)

• Example 4

• Example 4 Video

• Partial Fractions (Cover Up Method III)

• Example 5

• Example 5 Video

• Exercise 4.4

• Exercise 4.4 Recorded Solutions

• 5

### 4.5 Other Algebraic Substitutions

• Simplifying Integrands

• Example 1

• Example 1 Video

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Simplifying Integrands (Part II)

• Example 4

• Example 4 Video

• Exercise 4.5

• Exercise 4.5 Recorded Solutions

• 6

### 4.6 Trigonometric Functions I

• Powers of Sine and Cosine

• Example 1

• Example 1 Video

• Powers of Tangent and Secant

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Example 4

• Example 4 Video

• Powers of Cotangent and Cosecant

• Product to Sum Identities

• Example 5

• Example 5 Video

• Exercise 4.6

• Exercise 4.6 Recorded Solutions

• 7

### 4.7 Trigonometric Functions II

• Integrating with t-formulae

• Example 1

• Example 1 Video

• Trig Substitutions

• Example 2

• Example 2 Video

• Exercise 4.7

• Exercise 4.7 Recorded Solutions

• 8

### 4.8 Integration by Parts

• Integration by Parts (inc DETAIL)

• Example 1

• Example 1 Video

• Example 2

• Example 2 Video

• Integration by Parts (Reverse Chain Rule)

• Example 3

• Example 3 Video

• Exercise 4.8

• Exercise 4.8 Recorded Solutions

• 9

### 4.9 Recurrence Relationships

• Recurrence Relationships

• Example 1

• Example 1 Video

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Exercise 4.9

• Exercise 4.9 Recorded Solutions

• 10

### 4.10 Definite Integrals

• Definite Integrals

• Example 1

• Example 1 Video

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Example 4

• Example 4 Video

• Exercise 4.10

• Exercise 4.10 Recorded Solutions

## Instructor

Steven Howard

Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for over 25 years. He has also taught gifted and talented students online through xsel and Aurora College. He has a particular love and passion for Mathematics Extension 2, writing his own textbook and study resources for the new syllabus, which you can access from any of his courses. He loves finding more efficient techniques for solving mathematical questions, by trawling through other teachers' solutions or making up his own approaches when there must be a better way. Steve did 4 Unit Mathematics as a student, gaining a mark of 198/200 and training as an actuary. Working in an office in the city wasn't for him, so he went back to uni to retrain as a maths teacher then headed to the country, where he lives in an owner built mud house, with chickens, goats and rescued native birds (which you will sometimes hear in his recordings)!!