AP Calculus Book 3: Integration and Applications of Integration
AP Calculus Book 3: Integration and Applications of Integration
Master Integration and Its Real-World Applications
AP Calculus Book 3: Integration and Applications of Integration guides students through the essential concepts of integration, preparing them for success on the AP Calculus exam. This book builds on the foundations of limits, continuity, and differentiation to provide a complete understanding of integral calculus.
Understanding Integration
The book begins by introducing the concept of the integral, including indefinite and definite integrals. First, students learn techniques of integration such as substitution, integration by parts, and partial fractions. Next, it explains the Fundamental Theorem of Calculus and the connection between differentiation and integration.
Applications of Integration
In addition, the book emphasizes practical applications of integration. Students explore topics such as area under a curve, volume of solids of revolution, work, and average value of a function. Furthermore, real-world examples demonstrate how integration is used in physics, engineering, and economics.
Problem-Solving and Practice
AP Calculus Book 3 provides numerous examples, step-by-step solutions, and practice problems to reinforce understanding. Moreover, the book teaches strategies for tackling complex problems, enhancing analytical skills, and building confidence for the AP exam.
Exam Preparation
Finally, the book includes practice assessments that simulate the AP Calculus exam environment. Additionally, review questions allow students to evaluate progress, identify areas for improvement, and solidify their mastery of integration and its applications.
Whether preparing for the AP exam or aiming to strengthen calculus skills, AP Calculus Book 3: Integration and Applications of Integration is an essential resource for mastering one of the most important topics in calculus.
Course Features
- Lectures 21
- Quizzes 21
- Duration 52 weeks
- Skill level All levels
- Language English
- Students 285
- Assessments Yes
- 4 Sections
- 21 Lessons
- 52 Weeks
- Chapter one: Integration16
- 1.11.1: Antiderivatives and Indefinite Integrals
- 1.2Antiderivatives and Indefinite integrals Quiz10 Minutes4 Questions
- 1.31.2: Riemann Sum and Area Approximation
- 1.4Riemann Sum and Area Approximation Quiz15 Minutes6 Questions
- 1.51.3: Definite Integral, Area Under a Curve, and Application
- 1.6Definite Integral, Area Under a Curve, and Application Quiz20 Minutes10 Questions
- 1.71.4: Properties of Definite Integral
- 1.8Properties of Definite Integral Quiz10 Minutes4 Questions
- 1.91.5: Trapezoidal Rule
- 1.10Trapezoidal Rule Quiz10 Minutes5 Questions
- 1.111.6: Fundamental Theorem of Calculus
- 1.12Fundamental Theorem of Calculus Quiz20 Minutes10 Questions
- 1.131.7: Integration by Substitution
- 1.14Integration by Substitution Quiz15 Minutes7 Questions
- 1.151.8: Integration of Exponential and Logarithmic Functions
- 1.16Integration of Exponential and Logarithmic Functions Quiz15 Minutes7 Questions
- Chapter Two: Applications of Integration12
- 2.12.1: Area of Region Between Two Curves
- 2.2Area of Region Between Two Curves Quiz10 Minutes4 Questions
- 2.32.2: Volumes by Disk and Washers
- 2.4Volumes by Disk and Washers Quiz15 Minutes8 Questions
- 2.52.3: Volumes of Solids with Known Cross Sections
- 2.6Volumes of Solids with Known Cross Sections Quiz15 Minutes7 Questions
- 2.72.4: The Total Change Theorem (Application of FTC)
- 2.8The Total Change Theorem Quiz10 Minutes5 Questions
- 2.92.5: Motion of a Particle, Distance, and Displacement
- 2.10Motion of a Particle, Distance, and Displacement Quiz20 Minutes9 Questions
- 2.112.6: Average Value of a Function
- 2.12Average 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
