M12 Unit 7: Principles of Integral Evaluation

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Lesson 7.1: An Overview of Integration Methods 2 Topics

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•Topic 7.1.1: Methods for Approaching Integration Problems

•Topic 7.1.2: A Review of Familiar Integration Formulas

LESSON 7.2: Integration by Parts 6 Topics | 7 Quizzes

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•Topic 7.2.1: The Product Rule and Integration by Parts

Topic 7.2.1 Self-Quiz (Integration by Parts)

• Topic 7.2.2: Guideline for Integration by Parts

Topic 7.2.2 Self-Quiz (Guideline for Integration by Parts)

• Topic 7.2.3: Repeated Integration by Parts

Topic 7.2.3 Self-Quiz (Repeated Integration by Parts)

• Topic 7.2.4: A Tabular Method for Repeated Integration by Parts

Topic 7.2.4 Self-Quiz (A Tabular Method for Repeated Integration by Parts)

• Topic 7.2.5: Integration by Parts for Definite Integrals

Topic 7.2.5 Self-Quiz (Integration by Parts for Definite Integrals)

• Topic 7.2.6: Reduction Formulas

Topic 7.2.6 Self-Quiz (Reduction Formulas)

Lesson 7.2 Quiz (10 Marks)

Lesson 7.3- Integrating Trigonometric Functions 5 Topics | 5 Quizzes

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• Topic 7.3.1: Integrating Powers of Sine and Cosine

Topic 7.3.1 Self-Quiz (Integrating Power of Sine and Cosine)

• Topic 7.3.2: Integrating Products of Sines and Cosines

Topic 7.3.2 Self-Quiz (Integrating Products of Sines and Cosines)

• Topic 7.3.3: Integrating Powers of Tangent and Secant

Topic 7.3.3 Self-Quiz (Integrating Powers of Tangent and Secant)

• Topic 7.3.4: Integrating Products of Tangents and Secants

Topic 7.3.4 Self-Quiz (Integrating Products of Tangents and Secants)

• Topic 7.3.5: 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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• Topic 7.4.1: The Method of Trigonometric Substitution

Topic 7.4.1 Self-Quiz (The Method of Trigonometric Substitution)

Topic 7.4.2: Integrals Involving ax^2+bx+c

Topic 7.4.2 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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• Topic 7.5.1: Partial Fractions

Topic 7.5.1 Self-Quiz (Partial Fractions)

• Topic 7.5.2: Finding the Form of a Partial Fraction Decomposition

Topic 7.5.2 Self-Quiz (Finding the Form of a Partial Fraction Decomposition)

• Topic 7.5.3: Integrating Improper Rational Functions

Topic 7.5.3 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 7.6.1: Perfect Matches

Topic 7.6.1 Self-Quiz (Perfect Matches)

• Topic 7.6.2: Matches Requiring Substitutions

Topic 7.6.2 Self-Quiz (Matches Requiring Substitutions)

• Topic 7.6.3: Matches Requiring Reduction Formulas

• Topic 7.6.4: Special Substitutions

Topic 7.6.4 Self-Quiz (Special Substitutions)

• Topic 7.6.5: Integrating with Computer Algebra Systems

Topic 7.6.5 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 7.7.1: A Review of Riemann Sum Approximation

Topic 7.7.1 Self-Quiz (A Review of Riemann Sum Approximation)

• Topic 7.7.2: Trapezoidal Approximation

Topic 7.7.2 Self-Quiz (Trapezoidal Approximation)

• Topic 7.7.3: Simpson’s Rule

Topic 7.7.3 Self-Quiz (Simpson’s Rule)

• Topic 7.7.4: Error Bounds

Topic 7.7.4 Self-Quiz (Error Bounds)

• Topic 7.7.5: Comparison of the Three Methods

Lesson 7.7 Quiz (10 Marks)

Lesson 7.8: Improper Integrals 2 Topics | 2 Quizzes

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• Topic 7.8.1: Integrals Over Infinite Intervals

Topic 7.8.1 Self-Quiz (Integrals over Infinite Intervals)

• Topic 7.8.2: Integrals whose Integrands have Infinite Discontinuities

Topic 7.8.2 Self-Quiz (Integrals whose Integrands have Infinite Discontinuities)

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