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)
Previous Lesson
Next Lesson

Lesson 7.5- Integrating Rational Functions by Partial Fractions

M12 Unit 7: Principles of Integral Evaluation Lesson 7.5- Integrating Rational Functions by Partial Fractions

A rational function is a ratio of two polynomials . In this lesson we will give a general method for integrating rational functions that is based on the idea of decomposing a rational function into a sum of simple rational functions that can be integrated by the methods studied in earlier sections.

Lesson Content
0% Complete 0/3 Steps
Previous Lesson
Back to Course
Next Lesson