M12 Unit 7: Principles of Integral Evaluation – Tulip Intl. College

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Lesson 7.1- An Overview of Integration Methods 2 Topics

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Lesson Content

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• 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

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Lesson Content

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• 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

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Lesson Content

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• 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

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Lesson Content

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• 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

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Lesson Content

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• 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

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• 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

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• 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

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Lesson Content

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• 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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