AP Calculus Book 3: Integration and Applications of Integration
The AP Calculus Grey Module, “Integration and Applications,” is a vital part of the curriculum. It aims to deepen students’ understanding of integral calculus, focusing on mathematical concepts related to integration and enhancing their proficiency in calculus for the AP exam.
Guiding students through the study of integration—a fundamental calculus concept—the Grey Module moves beyond differentiation basics. It introduces them to the sophisticated realm of integration, shifting the focus from instantaneous rates of change to the total change over intervals.
Within integration, the Grey Module covers definite and indefinite integrals, various techniques, and the geometric interpretation. It helps students explore the fundamental theorem of calculus, establishing a vital connection between differentiation and integration.
A significant emphasis is on the practical applications of integration. Through examples and problems, students apply integration to solve issues related to area, volume, and other physical quantities. They explore the use of definite integrals in calculating accumulated change, enabling them to model and analyze dynamic processes in physics, economics, and biology.
Moreover, the Grey Module introduces advanced integration techniques. This includes integration by parts, partial fraction decomposition, and improper integrals. These additions expand students’ toolkit for solving a broader range of integrals, enhancing their problem-solving skills.
To further understanding, the module incorporates interactive learning methods. Practical examples, hands-on activities, and collaborative problem-solving are used. Assessments encompass tasks such as problem sets, quizzes, and comprehensive exams, evaluating students’ mastery of integration concepts and their ability to apply them.
Course Features
- Lectures 21
- Quizzes 21
- Duration 52 weeks
- Skill level All levels
- Language English
- Students 274
- Assessments Yes
Curriculum
- 4 Sections
- 21 Lessons
- 52 Weeks
- Chapter one: Integration16
- 1.01.1: Antiderivatives and Indefinite Integrals
- 1.1Antiderivatives and Indefinite integrals Quiz10 Minutes4 Questions
- 1.21.2: Riemann Sum and Area Approximation
- 1.3Riemann Sum and Area Approximation Quiz15 Minutes6 Questions
- 1.41.3: Definite Integral, Area Under a Curve, and Application
- 1.5Definite Integral, Area Under a Curve, and Application Quiz20 Minutes10 Questions
- 1.61.4: Properties of Definite Integral
- 1.7Properties of Definite Integral Quiz10 Minutes4 Questions
- 1.81.5: Trapezoidal Rule
- 1.9Trapezoidal Rule Quiz10 Minutes5 Questions
- 1.101.6: Fundamental Theorem of Calculus
- 1.11Fundamental Theorem of Calculus Quiz20 Minutes10 Questions
- 1.121.7: Integration by Substitution
- 1.13Integration by Substitution Quiz15 Minutes7 Questions
- 1.141.8: Integration of Exponential and Logarithmic Functions
- 1.15Integration of Exponential and Logarithmic Functions Quiz15 Minutes7 Questions
- Chapter Two: Applications of Integration12
- 2.02.1: Area of Region Between Two Curves
- 2.1Area of Region Between Two Curves Quiz10 Minutes4 Questions
- 2.22.2: Volumes by Disk and Washers
- 2.3Volumes by Disk and Washers Quiz15 Minutes8 Questions
- 2.42.3: Volumes of Solids with Known Cross Sections
- 2.5Volumes of Solids with Known Cross Sections Quiz15 Minutes7 Questions
- 2.62.4: The Total Change Theorem (Application of FTC)
- 2.7The Total Change Theorem Quiz10 Minutes5 Questions
- 2.82.5: Motion of a Particle, Distance, and Displacement
- 2.9Motion of a Particle, Distance, and Displacement Quiz20 Minutes9 Questions
- 2.102.6: Average Value of a Function
- 2.11Average Value of a Function Quiz12 Minutes6 Questions
- Chapter Three: Techniques of Integration8
- 3.13.1 : Basic Integration Rules
- 3.2Basic Integration Rules Quiz10 Minutes5 Questions
- 3.33.2: Trigonometric Integrals
- 3.4Trigonometric Integrals Quiz10 Minutes5 Questions
- 3.53.3: Trigonometric Substitution
- 3.6Trigonometric Substitution Quiz10 Minutes5 Questions
- 3.73.4: L’Hospital’s Rule
- 3.8L’Hospital’s Rule Quiz15 Minutes7 Questions
- Chapter 4: Further Applications of Integration6