Chapter 7: Techniques of Integration
Course
MATH162 (Calculus II)
Overview
This chapter covers Techniques of Integration from Stewart Calculus 9th Edition.
Each section contains:
- Skill breakdowns with learning objectives
- Practice problems at multiple difficulty levels
- Links to related skills and prerequisites
Sections
Section 7.1: Integration by Parts
| Skill | Description | Difficulty |
|---|---|---|
| Integration by Parts Formula | Techniques of Integration | Intermediate |
| Integration by Parts: Definite Integrals | Techniques of Integration | Intermediate |
| Repeated Integration by Parts | Techniques of Integration | Intermediate |
Section 7.2: Trigonometric Integrals
| Skill | Description | Difficulty |
|---|---|---|
| Integrals of Powers of Secant and Tangent | Techniques of Integration | Intermediate |
| Integrals of Powers of Sine and Cosine | Techniques of Integration | Intermediate |
| Using Product-to-Sum Formulas | Techniques of Integration | Intermediate |
Section 7.3: Trigonometric Substitution
| Skill | Description | Difficulty |
|---|---|---|
| Trig Sub: √(a²+x²) | Techniques of Integration | Intermediate |
| Trig Sub: √(a²-x²) | Techniques of Integration | Intermediate |
| Trig Sub: √(x²-a²) | Techniques of Integration | Intermediate |
Section 7.4: Integration of Rational Functions by Partial Fractions
| Skill | Description | Difficulty |
|---|---|---|
| Improper Rational Functions | Techniques of Integration | Intermediate |
| Partial Fractions: Distinct Linear Factors | Techniques of Integration | Intermediate |
| Partial Fractions: Irreducible Quadratic Factors | Techniques of Integration | Intermediate |
| Partial Fractions: Repeated Linear Factors | Techniques of Integration | Intermediate |
Section 7.5: Strategy for Integration
| Skill | Description | Difficulty |
|---|---|---|
| Integration Strategy | Techniques of Integration | Intermediate |
| Using Integration Tables | Techniques of Integration | Intermediate |
Section 7.6: Using Tables and Technology
| Skill | Description | Difficulty |
|---|---|---|
| Using Technology for Integration | Techniques of Integration | Beginner |
Section 7.7: Approximate Integration
| Skill | Description | Difficulty |
|---|---|---|
| Comparing Numerical Methods | Techniques of Integration | Intermediate |
| Simpson’s Rule | Techniques of Integration | Intermediate |
| The Trapezoidal Rule | Techniques of Integration | Intermediate |
Section 7.8: Improper Integrals
| Skill | Description | Difficulty |
|---|---|---|
| Comparison Test for Integrals | Techniques of Integration | Advanced |
| Type 1: Infinite Limits | Techniques of Integration | Intermediate |
| Type 2: Discontinuous Integrands | Techniques of Integration | Intermediate |
Prerequisites
Before starting Chapter 7, review relevant prerequisite skills from earlier chapters.
| Previous | Up | Next |
|---|---|---|
| Chapter 6 | Home | Chapter 8 |