# Ch 11: Area Under the Curve and Integrals in AP Calculus: Tutoring Solution

The Area Under the Curve and Integrals chapter of this AP Calculus AB and BC Tutoring Solution is a flexible and affordable path to learning about the area under the curve and integrals. These simple and fun video lessons are each about five minutes long and they teach all the operations involving area under the curve and integrals required in a typical AP calculus course.

## How it works:

• Begin your assignment or other AP calculus work.
• Identify the area under the curve and integrals concepts that you're stuck on.
• Find fun videos on the topics you need to understand.
• Press play, watch and learn!
• Complete the quizzes to test your understanding.
• As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our AP calculus tutoring solution will benefit any student who is trying to learn area under the curve and integrals for AP calculus and earn better grades. This resource can help students including those who:

• Struggle with understanding summation notation, Riemann sums, average value theorem, arc lengths of functions or any other area under the curve and integrals topic
• Have limited time for studying
• Want a cost effective way to supplement their math learning
• Prefer learning math visually
• Find themselves failing or close to failing their area under the curve and integrals unit
• Want to get ahead in AP calculus

## Why it works:

• Engaging Tutors: We make learning about area under the curve and integrals for AP calculus simple and fun.
• Cost Efficient: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.
• Consistent High Quality: Unlike a live calculus tutor, these video lessons are thoroughly reviewed.
• Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about area under the curve and integrals on the go!
• Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

• Understand how to use summation notation.
• Use Riemann sums for functions and graphs.
• Identify and draw right, left, and middle Riemann sums.
• Become familiar with the trapezoid rule.
• Determine the limits of Riemann sums.
• Learn the definition of definite integrals.
• Calculate integrals using Riemann sums.
• Describe the linear properties of definite integrals.
• Explain the applications of the average value theorem.
• Discuss the relationship between antiderivatives and indefinite integrals.
• Take a look at the fundamental theorem of calculus.
• Find the arc length of a function.

11 Lessons in Chapter 11: Area Under the Curve and Integrals in AP Calculus: Tutoring Solution
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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