Chapter 4: Integrals
Course
MATH161 (Calculus I)
Overview
This chapter covers Integrals 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 4.1: The Area and Distance Problems
| Skill | Description | Difficulty |
|---|---|---|
| Riemann Sums | Integrals | Intermediate |
| Sigma Notation for Sums | Integration Foundations | Beginner |
| The Area Problem | Integrals | Intermediate |
| The Area and Distance Problems | Integration Foundations | Beginner |
| The Distance Problem | Integrals | Intermediate |
Section 4.2: The Definite Integral
| Skill | Description | Difficulty |
|---|---|---|
| Computing Riemann Sums | Integration | Intermediate |
| Evaluating Definite Integrals | Integrals | Intermediate |
| Properties of Definite Integrals | Integration | Intermediate |
| Properties of the Definite Integral | Integrals | Intermediate |
| The Definite Integral Definition | Integration | Intermediate |
| The Midpoint Rule | Integrals | Intermediate |
Section 4.3: The Fundamental Theorem of Calculus
| Skill | Description | Difficulty |
|---|---|---|
| Applying FTC | Integrals | Intermediate |
| FTC Part 1 | Integrals | Intermediate |
| FTC Part 1 with Chain Rule | Fundamental Theorem of Calculus | Intermediate |
| FTC Part 1: Differentiating Integrals | Fundamental Theorem of Calculus | Intermediate |
| FTC Part 2 | Integrals | Intermediate |
| FTC Part 2: Evaluating Definite Integrals | Fundamental Theorem of Calculus | Intermediate |
Section 4.4: Indefinite Integrals and the Net Change Theorem
| Skill | Description | Difficulty |
|---|---|---|
| Applications of Net Change | Integrals | Intermediate |
| Computing Indefinite Integrals | — | Intermediate |
| Displacement vs Total Distance | — | Intermediate |
| Displacement vs. Total Distance | Integration | Intermediate |
| Indefinite Integral Notation | — | Beginner |
| Indefinite Integrals | Integrals | Intermediate |
| Net Change Theorem | — | Intermediate |
Section 4.5: The Substitution Rule
| Skill | Description | Difficulty |
|---|---|---|
| Integrals of Symmetric Functions | Integration | Intermediate |
| Integration and Symmetry | Integrals | Intermediate |
| Substitution Strategies | Integrals | Intermediate |
| Substitution: Definite Integrals | Integrals | Intermediate |
| Substitution: Indefinite Integrals | Integrals | Intermediate |
| u-Substitution (Definite Integrals) | Integration | Intermediate |
| u-Substitution (Indefinite Integrals) | Integration | Intermediate |
Prerequisites
Before starting Chapter 4, review relevant prerequisite skills from earlier chapters.
| Previous | Up | Next |
|---|---|---|
| Chapter 3 | Home | Chapter 5 |