M12 Unit 7: Principles of Integral Evaluation

Lesson 7.1- An Overview of Integration Methods
2 Topics
• Topic 1: Methods for Approaching Integration Problems
• Topic 2: A Review of Familiar Integration Formulas
LESSON 7.2- Integration by Parts
6 Topics | 7 Quizzes
• Topic 1: The Product Rule and Integration by Parts
Topic 1 Self-Quiz (Integration by Parts)
• Topic 2: Guideline for Integration by Parts
Topic 2 Self-Quiz (Guideline for Integration by Parts)
• Topic 3: Repeated Integration by Parts
Topic 3 Self-Quiz (Repeated Integration by Parts)
• Topic 4: A Tabular Method for Repeated Integration by Parts
Topic 4 Self-Quiz (A Tabular Method for Repeated Integration by Parts)
• Topic 5: Integration by Parts for Definite Integrals
Topic 5 Self-Quiz (Integration by Parts for Definite Integrals)
• Topic 6: Reduction Formulas
Topic 6 Self-Quiz (Reduction Formulas)
Lesson 7.2 Quiz (10 Marks)
Lesson 7.3- Integrating Trigonometric Functions
5 Topics | 5 Quizzes
• Topic 1: Integrating Powers of Sine and Cosine
Topic 1 Self-Quiz (Integrating Power of Sine and Cosine)
• Topic 2: Integrating Products of Sines and Cosines
Topic 2 Self-Quiz (Integrating Products of Sines and Cosines)
• Topic 3: Integrating Powers of Tangent and Secant
Topic 3 Self-Quiz (Integrating Powers of Tangent and Secant)
• Topic 4: Integrating Products of Tangents and Secants
Topic 4 Self-Quiz (Integrating Products of Tangents and Secants)
• Topic 5: An Alternative Method for Integrating Powers of Sine, Cosine, Tangent and Secant
Lesson 7.3 Quiz (Integrating Trigonometric Functions) (10 Marks)
Lesson 7.4- Trigonometric Substitutions
2 Topics | 3 Quizzes
• Topic 1: The Method of Trigonometric Substitution
Topic 1 Self-Quiz (The Method of Trigonometric Substitution)
Topic 2: Integrals Involving ax^2+bx+c
Topic 2 Self-Quiz (Integrals Involving ax^2+bx+c)
Lesson 7.4 Quiz (10 Marks)
Lesson 7.5- Integrating Rational Functions by Partial Fractions
3 Topics | 4 Quizzes
• Topic 1: Partial Fractions
Topic 1 Self-Quiz (Partial Fractions)
• Topic 2: Finding the Form of a Partial Fraction Decomposition
Topic 2 Self-Quiz (Finding the Form of a Partial Fraction Decomposition)
• Topic 3: Integrating Improper Rational Functions
Topic 3 Self-Quiz (Integrating Improper Rational Functions)
Lesson 7.5 Quiz (10 Marks)
Lesson 7.6- Using Computer Algebra Systems and Tables of Integrals
5 Topics | 5 Quizzes
• Topic 1: Perfect Matches
Topic 1 Self-Quiz (Perfect Matches)
• Topic 2: Matches Requiring Substitutions
Topic 2 Self-Quiz (Matches Requiring Substitutions)
• Topic 3: Matches Requiring Reduction Formulas
• Topic 4: Special Substitutions
Topic 4 Self-Quiz (Special Substitutions)
• Topic 5: Integrating with Computer Algebra Systems
Topic 5 Self-Quiz (Integrating with Computer Algebra Systems)
Lesson 7.6 Quiz (10 Marks)
Lesson 7.7- Numerical Integration; Simpson’s Rule
5 Topics | 5 Quizzes
• Topic 1: A Review of Riemann Sum Approximation
Topic 1 Self-Quiz (A Review of Riemann Sum Approximation)
• Topic 2: Trapezoidal Approximation
Topic 2 Self-Quiz (Trapezoidal Approximation)
• Topic 3: Simpson’s Rule
Topic 3 Self-Quiz (Simpson’s Rule)
• Topic 4: Error Bounds
Topic 4 Self-Quiz (Error Bounds)
• Topic 5: Comparison of the Three Methods
Lesson 7.7 Quiz (10 Marks)
Lesson 7.8- Improper Integrals
2 Topics | 3 Quizzes
• Topic 1: Integrals Over Infinite Intervals
Topic 1 Self-Quiz (Integrals over Infinite Intervals)
• Topic 2: Integrals whose Integrands have Infinite Discontinuities
Topic 2 Self-Quiz (Integrals whose Integrands have Infinite Discontinuities)
Lesson 7.8 Quiz (10 Marks)
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Lesson 7.3- Integrating Trigonometric Functions

M12 Unit 7: Principles of Integral Evaluation Lesson 7.3- Integrating Trigonometric Functions

In the last session we derived reduction formulas for integrating positive integer powers of Sine, Cosine, Tangent and Secant. In this section, we will show how to work with these reduction formulas and we will discuss methods for integrating other kinds of integrals that involves trigonometric functions.

Lesson Content
0% Complete 0/5 Steps
• Topic 1: Integrating Powers of Sine and Cosine
Topic 1 Self-Quiz (Integrating Power of Sine and Cosine)
• Topic 2: Integrating Products of Sines and Cosines
Topic 2 Self-Quiz (Integrating Products of Sines and Cosines)
• Topic 3: Integrating Powers of Tangent and Secant
Topic 3 Self-Quiz (Integrating Powers of Tangent and Secant)
• Topic 4: Integrating Products of Tangents and Secants
Topic 4 Self-Quiz (Integrating Products of Tangents and Secants)
• Topic 5: An Alternative Method for Integrating Powers of Sine, Cosine, Tangent and Secant
Lesson 7.3 Quiz (Integrating Trigonometric Functions) (10 Marks)
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