Courses

AP (Advanced Placement) Calculus AB : Integration

This course offers an in-depth exploration of definite integrals and their real-world applications, along with an introduction to mathematical modeling using differential equations. You'll learn how to estimate areas under curves, apply the Fundamental Theorem of Calculus, and use integrals to compute areas, volumes, and net changes. The course also covers numerical integration techniques like the trapezoidal rule and applies integrals in scientific, statistical, and economic contexts. In the final section, you'll be introduced to differential equations, slope fields, exponential growth and decay, and how to model real-life problems mathematically. Each module includes assignments to reinforce your understanding through hands-on practice.

Age group: 15-19

Content

# 📘 Calculus Course Modules ## 📐 Definite Integrals ### 🔹 Introduction to Definite Integrals - Understanding the concept and purpose of definite integrals ### 🔹 Estimating with Finite Sums - Learn how to approximate areas under curves using finite sums ### 🔹 Calculate Definite Integrals - Techniques and strategies for computing definite integrals ### 🔹 Definite Integrals and Antiderivatives - Connecting integration and differentiation ### 🔹 The Fundamental Theorem of Calculus - Explore the cornerstone theorem linking derivatives and integrals ### 🔹 The Trapezoidal Rule - Apply numerical integration using the trapezoidal approximation ### 📝 Definite Integrals: Assignment - Test your understanding through practical problems --- ## 🧮 Applications of Definite Integrals ### 🔹 Introduction to Applications of Definite Integrals - Overview of real-world uses of integrals ### 🔹 Integral as Net Change - Use integrals to measure net change in various contexts ### 🔹 Areas in the Plane - Compute the area under and between curves ### 🔹 Volumes - Use integration to find the volume of solids ### 🔹 Applications from Science and Statistics - Real-life applications in physics, biology, economics, and data science ### 🔹 L'Hôpital's Rule and Other Applications - Understand limits and advanced applications related to integrals ### 📝 Applications of Definite Integrals: Assignment - Practice applying concepts to solve contextual problems --- ## 🧾 Mathematical Modeling Using Differential Equations ### 🔹 Introduction to Mathematical Modeling - Using differential equations to model real-world phenomena ### 🔹 Slope Fields - Graphical representation of differential equations ### 🔹 Antidifferentiation by Substitution - A technique for solving integrals via substitution ### 🔹 Exponential Growth and Decay - Modeling population, radioactive decay, and more ### 📝 Differential Equation: Assignment - Apply mathematical modeling to real scenarios

Prerequisites

Should have studied algebra, geometry, trigonometry, analytic geometry, and elementary functions
Should understand the properties of linear, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions
Should familiar with basic concepts of differentiation

Objectives

Improper Integrals: Learn to evaluate improper integrals, including those with infinite limits of integration and unbounded integrands, using advanced techniques and concepts.
Fundamental Theorem of Calculus: Apply the Fundamental Theorem of Calculus to evaluate integrals and understand the relationship between differentiation and integration.
Applications of Integrals: Explore complex applications of integrals, including calculating areas, volumes, work, and other physical quantities.
Techniques of Integration: Gain proficiency in advanced techniques of integration, such as integration by parts, partial fractions, and trigonometric substitution.
Mastery of Definite and Indefinite Integrals: Develop a deep understanding of both definite and indefinite integrals, including their properties and applications.

Outcomes

You will learn to evaluate definite integrals
You will know the connection between differentiation and integration
You will gain an understanding of exponential growth/decay
You will master solving wide range of problems involving rate of change, volume of solids, area enclosed by the curve, and many more
You will get skillful in solving differential equations

Why learn with Enthuziastic?

Here's why more and more people are joining Enthuziastic

Personalized Lessons

Customize your lessons to meet your individual goals.

Expert Teachers

Top rated teachers to guide you through the learning process.

Flexible Timings

Attend classes anytime, anywhere. Make your own schedule.

Easy Rescheduling

Manage holidays or conflicting appointments easily by rescheduling classes.

Complete Support

A compassionate support team to listen to your needs.

Homework & Assignments

Reinforce your learning with practical homework and hands-on assignments.

Completion Certificate

You will get a certificate for the completion of the course.

Group Discussion & Peer Learning

Collaborate with peers through discussions and shared learning experiences.

Access to Alumni Community

Join a vibrant alumni network for support, insights, and continued learning.

Post-Course Support & Career Guidance

Get expert support and career advice even after the course ends.

How it works?

Enroll

Enroll for the course of your liking by selecting 1:1 or group classes. Choose the type of instructor you want to learn with.

Schedule

Download Enthu app and schedule classes for the day and time that works best for you. You own your learning schedule.

Learn

Join classes on Zoom and start learning with lessons customized for you. Make most of our student success program.

Value Proposition

We offer a diverse range of interactive classes, ensuring accessible and personalized education for everyone, anytime, anywhere.

Carefully Curated Expert Instructors

All courses are taught by our expert instructors who are carefully chosen with a rigorous < 1% acceptance rate. For every 100 tutors interviewed, only 1 is chosen, ensuring you get the best.

Engaging and Interactive Classes

Each session is designed to be dynamic and captivating, ensuring the learner stays excited and engaged throughout.

Progress Reports

Our team works hard behind the scenes to create and maintain a meticulously detailed progress report for each learner as they progress through the sessions.

Session Recordings

The recordings of each session are automatically available in the app after 24 hours of each session, they are extremely helpful for revisions.

Certificates

Some rewards are necessary for motivating learners and Enthuziastic awards dedicated learners with official certificate of completion and if they win in any of our regular competitions, they are awarded the respective winners certificates.

Feedback and Assignments

Parents/Learners provide us regular feedback after every session through a formal submission in the app, this helps us customize the learning path after every session according to how the learners are responding to the tutoring.

Chat Communication

Connect with instructors and peer learners directly via our app's dedicated chat group for every batch fostering a community experience while learning together.

24/7 Support

We take great pride in our service delivery. We're here for you round the clock to address any questions or concerns.

Quality & Affordability

The entire Enthuziastic team strives hard to bring you high quality learning at affordable prices. Because of the support of learners like yourself, we continue to grow our offerings and keep making them more and more affordable.

Personal Family Buddy

You will be assigned a personal family buddy, whom you can continuously stay in touch through and beyond your learners learning journey. Whatever your needs are you can always reach out to your Family Buddy/Student Success Manager whose only job is to make your learning journey successful.

Carefully Curated Expert Instructors

All courses are taught by our expert instructors who are carefully chosen with a rigorous < 1% acceptance rate. For every 100 tutors interviewed, only 1 is chosen, ensuring you get the best.

Engaging and Interactive Classes

Each session is designed to be dynamic and captivating, ensuring the learner stays excited and engaged throughout.

Progress Reports

Our team works hard behind the scenes to create and maintain a meticulously detailed progress report for each learner as they progress through the sessions.

Session Recordings

The recordings of each session are automatically available in the app after 24 hours of each session, they are extremely helpful for revisions.

Certificates

Feedback and Assignments

Chat Communication

Connect with instructors and peer learners directly via our app's dedicated chat group for every batch fostering a community experience while learning together.

24/7 Support

We take great pride in our service delivery. We're here for you round the clock to address any questions or concerns.

Quality & Affordability

Personal Family Buddy

Frequently asked questions (FAQs)

Expand all

This course is perfect for high school and early college students studying calculus, or anyone who wants to strengthen their grasp of integration and differential equations.

Yes, basic knowledge of derivatives and introductory integration will be very helpful for understanding the material.

The course connects calculus concepts to real-life scenarios, such as population modeling, motion, energy consumption, and data trends in science and economics.

Absolutely! The course includes sections on finding areas under curves and volumes of solids using definite integrals.

Yes, each major topic ends with a dedicated assignment to help you apply what you've learned and test your problem-solving skills.

Do you have any questions?

Fill this form and we will respond back, on priority.

This Includes

12 live tutoring sessions

Access on mobile and web

Certificate of completion

Hands-on Exercises & Practical Projects

Personalized Feedback & Coaching

Session Recordings for Rewatching

Typical Price (for 2 seats)

30-Day Money-Back Guarantee

Courses

AP (Advanced Placement) Calculus AB : Integration

Age group: 15-19

Content

Prerequisites

Should have studied algebra, geometry, trigonometry, analytic geometry, and elementary functions
Should understand the properties of linear, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions
Should familiar with basic concepts of differentiation

Objectives

Improper Integrals: Learn to evaluate improper integrals, including those with infinite limits of integration and unbounded integrands, using advanced techniques and concepts.
Fundamental Theorem of Calculus: Apply the Fundamental Theorem of Calculus to evaluate integrals and understand the relationship between differentiation and integration.
Applications of Integrals: Explore complex applications of integrals, including calculating areas, volumes, work, and other physical quantities.
Techniques of Integration: Gain proficiency in advanced techniques of integration, such as integration by parts, partial fractions, and trigonometric substitution.
Mastery of Definite and Indefinite Integrals: Develop a deep understanding of both definite and indefinite integrals, including their properties and applications.

Outcomes

You will learn to evaluate definite integrals
You will know the connection between differentiation and integration
You will gain an understanding of exponential growth/decay
You will master solving wide range of problems involving rate of change, volume of solids, area enclosed by the curve, and many more
You will get skillful in solving differential equations

Why learn with Enthuziastic?

Here's why more and more people are joining Enthuziastic

Personalized Lessons

Customize your lessons to meet your individual goals.

Expert Teachers

Top rated teachers to guide you through the learning process.

Flexible Timings

Attend classes anytime, anywhere. Make your own schedule.

Easy Rescheduling

Manage holidays or conflicting appointments easily by rescheduling classes.

Complete Support

A compassionate support team to listen to your needs.

Homework & Assignments

Reinforce your learning with practical homework and hands-on assignments.

Completion Certificate

You will get a certificate for the completion of the course.

Group Discussion & Peer Learning

Collaborate with peers through discussions and shared learning experiences.

Access to Alumni Community

Join a vibrant alumni network for support, insights, and continued learning.

Post-Course Support & Career Guidance

Get expert support and career advice even after the course ends.

How it works?

Enroll

Enroll for the course of your liking by selecting 1:1 or group classes. Choose the type of instructor you want to learn with.

Schedule

Download Enthu app and schedule classes for the day and time that works best for you. You own your learning schedule.

Learn

Join classes on Zoom and start learning with lessons customized for you. Make most of our student success program.

Value Proposition

We offer a diverse range of interactive classes, ensuring accessible and personalized education for everyone, anytime, anywhere.

Carefully Curated Expert Instructors

All courses are taught by our expert instructors who are carefully chosen with a rigorous < 1% acceptance rate. For every 100 tutors interviewed, only 1 is chosen, ensuring you get the best.

Engaging and Interactive Classes

Each session is designed to be dynamic and captivating, ensuring the learner stays excited and engaged throughout.

Progress Reports

Our team works hard behind the scenes to create and maintain a meticulously detailed progress report for each learner as they progress through the sessions.

Session Recordings

The recordings of each session are automatically available in the app after 24 hours of each session, they are extremely helpful for revisions.

Certificates

Feedback and Assignments

Chat Communication

Connect with instructors and peer learners directly via our app's dedicated chat group for every batch fostering a community experience while learning together.

24/7 Support

We take great pride in our service delivery. We're here for you round the clock to address any questions or concerns.

Quality & Affordability

Personal Family Buddy

Carefully Curated Expert Instructors

All courses are taught by our expert instructors who are carefully chosen with a rigorous < 1% acceptance rate. For every 100 tutors interviewed, only 1 is chosen, ensuring you get the best.

Engaging and Interactive Classes

Each session is designed to be dynamic and captivating, ensuring the learner stays excited and engaged throughout.

Progress Reports

Our team works hard behind the scenes to create and maintain a meticulously detailed progress report for each learner as they progress through the sessions.

Session Recordings

The recordings of each session are automatically available in the app after 24 hours of each session, they are extremely helpful for revisions.

Certificates

Feedback and Assignments

Chat Communication

Connect with instructors and peer learners directly via our app's dedicated chat group for every batch fostering a community experience while learning together.

24/7 Support

We take great pride in our service delivery. We're here for you round the clock to address any questions or concerns.

Quality & Affordability

Personal Family Buddy

Frequently asked questions (FAQs)

Expand all

This course is perfect for high school and early college students studying calculus, or anyone who wants to strengthen their grasp of integration and differential equations.

Yes, basic knowledge of derivatives and introductory integration will be very helpful for understanding the material.

The course connects calculus concepts to real-life scenarios, such as population modeling, motion, energy consumption, and data trends in science and economics.

Absolutely! The course includes sections on finding areas under curves and volumes of solids using definite integrals.

Yes, each major topic ends with a dedicated assignment to help you apply what you've learned and test your problem-solving skills.