Further Integration
112 videos • 18,679 views • by Eddie Woo
1
Integrating Rational Polynomials (Example)
Eddie Woo
Download
2
Partial Fractions (example with cubic denominator)
Eddie Woo
Download
3
Partial Fractions for Integrating Rational Polynomials
Eddie Woo
Download
4
Partial Fractions w/ Perfect Square Denominators
Eddie Woo
Download
5
Rearranging Rational Polynomials w/ Division Transformation
Eddie Woo
Download
6
Deriving Integration by Parts
Eddie Woo
Download
7
Integration by Parts - Example 1: x cos x
Eddie Woo
Download
8
Integration by Parts - Example 2: x*e^x & x²*e^x
Eddie Woo
Download
9
Integration by Parts - Example 3: ln x
Eddie Woo
Download
10
Integration by Parts - Example 4: e^x * sin x
Eddie Woo
Download
11
An unusual integral with two very different solutions?
Eddie Woo
Download
12
Integration by Parts - Example 5: sin¯¹(x)
Eddie Woo
Download
13
Integrals that lead to Logarithmic Functions
Eddie Woo
Download
14
Introduction to Recurrence Relations
Eddie Woo
Download
15
Recurrence Relation Example: Integrating (sin x)^n
Eddie Woo
Download
16
Recurrence Relations without IBP (1 of 2): (tan x)^n
Eddie Woo
Download
17
Recurrence Relations without IBP (2 of 2): (x^n)/(x+1)
Eddie Woo
Download
18
Sometimes integration by parts is a bad idea...
Eddie Woo
Download
19
Integrating with t-results (1 of 3): Example integral through identities
Eddie Woo
Download
20
Integrating with t-results (2 of 3): Changing the variable of integration
Eddie Woo
Download
21
Integrating with t-results (3 of 3): Further example
Eddie Woo
Download
22
Why do logarithmic functions have absolute value signs after integration?
Eddie Woo
Download
23
Integrating √[x/(1-x)] by Trigonometric Substitution
Eddie Woo
Download
24
Correction of Wrong Solution from Fitzpatrick (integration question)
Eddie Woo
Download
25
Tricky Recurrence Relation with Unexpected Algebraic Manipulation
Eddie Woo
Download
26
Evaluating Recurrence Relations
Eddie Woo
Download
27
Proving Properties of Definite Integrals (1 of 2)
Eddie Woo
Download
28
Proving Properties of Definite Integrals (2 of 2)
Eddie Woo
Download
29
3 Definite Integrals Evaluated by Trigonometric Substitution
Eddie Woo
Download
30
Integrating √(16-x²)/x² by Trigonometric Substitution
Eddie Woo
Download
31
Integrating √[(1+x)/(1-x)] by Trigonometric Substitution
Eddie Woo
Download
32
Evaluating Definite Integral w/ t-results
Eddie Woo
Download
33
Integral of sin(x)tan²(x): Three Approaches
Eddie Woo
Download
34
Proving Inequality from an Increasing Function
Eddie Woo
Download
35
Proving Inequality from Prior Integral
Eddie Woo
Download
36
Proving that a function is increasing
Eddie Woo
Download
37
Using Properties of Definite Integrals: Trigonometric Integrand (1 of 2)
Eddie Woo
Download
38
Determining Algebraic Recurrence Relation
Eddie Woo
Download
39
Expressing I(n) without Recursion
Eddie Woo
Download
40
Using Properties of Definite Integrals: Trigonometric Integrand (2 of 2)
Eddie Woo
Download
41
Harder (Ext 2) Integral Requiring Substitution
Eddie Woo
Download
42
Harder (Ext 2) Integral Question (1 of 2: Manipulating the Recurrence Relation)
Eddie Woo
Download
43
Harder (Ext 2) Integral Question (2 of 2: Evaluating Related Limiting Sum)
Eddie Woo
Download
44
Partial Fractions (1 of 3: Introducing an identity to simplify a quadratic denominator)
Eddie Woo
Download
45
Partial Fractions (2 of 3: An alternative method to find introduced variables)
Eddie Woo
Download
46
Partial Fractions (3 of 3: How to use Partial Fractions to split fractions with Quadratic Numerator)
Eddie Woo
Download
47
Partial Fractions: Quadratic Factors (1 of 2: Issues with non-linear denominator factors)
Eddie Woo
Download
48
Partial Fractions: Quadratic Factors (2 of 2: Problems with Quadratic Factors and Solution)
Eddie Woo
Download
49
Partial Fraction: Repeated Linear Factors (Technique for Breaking down into partial fractions)
Eddie Woo
Download
50
Integration of Square Root Function (1 of 2: Using a Trig Substitution to help with integration)
Eddie Woo
Download
51
Integration of Square Root Function (2 of 2: What is this kind of integral solving for?)
Eddie Woo
Download
52
Further Integration (1 of 2: Brief Overview of Extension II Integration)
Eddie Woo
Download
53
Further Integration (2 of 2: Integrating Trig Functions without given substitution)
Eddie Woo
Download
54
Further Integration [Continued] (1 of 3: Using Double Angle & Completing the Square to integrate)
Eddie Woo
Download
55
Further Integration [Continued] (2 of 3: Adding and subtracting a constant to simplify integral)
Eddie Woo
Download
56
Further Integration [Continued] (3 of 3: 'Breaking Apart' Integrals to simplify for integration)
Eddie Woo
Download
57
Partial Fractions & Integration (Using Partial Fractions to simplify an integral for evaluation)
Eddie Woo
Download
58
Harder Reverse Chain Rule Integral (Using a Substitution and Restrictions to evaluate)
Eddie Woo
Download
59
Proving a Result from the Standard Integrals (1 of 3: Differentiate, Hence Integrate Proof)
Eddie Woo
Download
60
Proving a Result from the Standard Integrals (2 of 3: Substituting tan to simplify the integral)
Eddie Woo
Download
61
Proving a Result from the Standard Integrals (3 of 3: Using Partial Fractions to simplify sec)
Eddie Woo
Download
62
Integration with t-results (1 of 2: Changing the variable of integration)
Eddie Woo
Download
63
Integration with t-results (2 of 2: Dealing with the integral in t)
Eddie Woo
Download
64
Integration by Parts (1 of 3: Deriving the Formula)
Eddie Woo
Download
65
Integration by Parts (2 of 3: How to choose u & dv)
Eddie Woo
Download
66
Integration by Parts (3 of 3: Integral of sin¯¹(x))
Eddie Woo
Download
67
Integration by t results (Explanation of Harder Question)
Eddie Woo
Download
68
Integration by Parts (What to choose for u and dv for integration by parts?)
Eddie Woo
Download
69
Integration with t Results (1 of 2: Changing the variable to solve with t results)
Eddie Woo
Download
70
Integration with t Results (2 of 2: Simplifying the integral before applying t results)
Eddie Woo
Download
71
Recurrence Relations (1 of 4: Introduction to Recurrence relations with introductory examples)
Eddie Woo
Download
72
Recurrence Relations (2 of 4: Considering if the question consists of some arbitrary power of n)
Eddie Woo
Download
73
Recurrence Relations (3 of 4: Applying to Trigonometric Functions raised to power of n)
Eddie Woo
Download
74
Recurrence Relations (4 of 4: Integration by parts with definite integrals)
Eddie Woo
Download
75
Evaluating Recurrence Relations (1 of 4: When do you apply Recurrence Relations?)
Eddie Woo
Download
76
Evaluating Recurrence Relations (2 of 4: Using Integration of parts to build recurring pattern)
Eddie Woo
Download
77
Evaluating Recurrence Relations (3 of 4: Using Recurring Pattern to group Relation in a series)
Eddie Woo
Download
78
Evaluating Recurrence Relations (4 of 4: Finding a term free of integrals)
Eddie Woo
Download
79
Extension 2 Exam Review (1 of 7: Integration by Substitution, Partial Fractions)
Eddie Woo
Download
80
Extension 2 Exam Review (2 of 7: Recurrence Relation, Graph Transformations)
Eddie Woo
Download
81
Mathematics Extension 1 Exam Review (1 of 3: Integration by substitution)
Eddie Woo
Download
82
Integration by Parts (2 of 2: When the integrand doesn't look like a product)
Eddie Woo
Download
83
Integration by Parts (1 of 2: Arranging the integral with DETAIL)
Eddie Woo
Download
84
Integration with Quadratic Denominators (3 of 3: Rationalising the numerator)
Eddie Woo
Download
85
Integration with Quadratic Denominators (2 of 3: Distinguishing characteristics)
Eddie Woo
Download
86
Integration with Quadratic Denominators (1 of 3: Introduction - why are they challenging?)
Eddie Woo
Download
87
Partial Fractions (3 of 3: Three solution methods)
Eddie Woo
Download
88
Partial Fractions (2 of 3: What are they?)
Eddie Woo
Download
89
Partial Fractions (1 of 3: Review questions)
Eddie Woo
Download
90
Integration by Unspecified Substitution (3 of 3: Trigonometric example)
Eddie Woo
Download
91
Integration by Unspecified Substitution (2 of 3: Square root example)
Eddie Woo
Download
92
Integration by Unspecified Substitution (1 of 3: Introductory example)
Eddie Woo
Download
93
Intro to Further Integration (2 of 2: Foundational examples)
Eddie Woo
Download
94
Intro to Further Integration (1 of 2: Expanding on prior learning)
Eddie Woo
Download
95
Recurrence Relations (3 of 3: Trigonometric examples)
Eddie Woo
Download
96
Recurrence Relations (2 of 3: Exponential example)
Eddie Woo
Download
97
Recurrence Relations (1 of 3: Introduction & logarithmic example)
Eddie Woo
Download
98
Recurrence Relation - worked example (1 of 2: Integration by parts)
Eddie Woo
Download
99
Recurrence Relation - worked example (2 of 2: Connecting the integrals)
Eddie Woo
Download
100
Logarithmic integral with recurrence relation (Exam Question 4 of 10)
Eddie Woo
Download
101
Integral via partial fractions (Exam Question 9 of 10)
Eddie Woo
Download
102
Reverse chain rule integral (Exam Question 7 of 10)
Eddie Woo
Download
103
Recurrence Relation (1 of 6: Setting up integration by parts)
Eddie Woo
Download
104
Recurrence Relation (2 of 6: Relating consecutive integrals)
Eddie Woo
Download
105
Recurrence Relation (3 of 6: Establishing the pattern)
Eddie Woo
Download
106
Integrating sec⁸θ
Eddie Woo
Download
107
Inequality proof from integration by parts
Eddie Woo
Download
108
Recurrence Relation (4 of 6: Expressing without integrals)
Eddie Woo
Download
109
Recurrence Relation (5 of 6: Trigonometric substitution)
Eddie Woo
Download
110
Recurrence Relation (6 of 6: Proving an inequality)
Eddie Woo
Download
111
Integration: how to choose boundaries with trigonometric substitution
Eddie Woo
Download
112
Integration by substitution (two ways)
Eddie Woo
Download