Integrals Teacher Resources
Find Integrals lesson plans and worksheets
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Historical Reflections on the Fundamental Theorem Of (Integral) Calculus
11th - 12th
Highlight the process of mathematical discovery for your classes. This lesson examines the development of the Fundamental Theorem of Calculus over time. Understanding the history of the theorem helps create a better understanding of the...
Properties of the Definite Integral
8 mins 11th - Higher Ed
What are the properties that can be associated with the definite integral? The AP Calculus video lists nine properties of the definite integral and provides explanations of why the properties hold for integrals in language that is simple...
Study Guide for the Advanced Placement Calculus AB Examination
11th - 12th CCSS: Adaptable
Is this going to be on the test? A calculus study guide provides an organized list of important topics and a few examples with answers. The topics include elementary functions, limits, differential calculus, and integral calculus,...
Integration and the Fundamental Theorem of Calculus | Essence of Calculus, Chapter 8
21 mins 11th - Higher Ed
Integrate a great resource into your lesson plans. The eighth video in an 11-part series explains integration and the relationship between derivatives and integrals. The relationship between a car's velocity and its travel distance helps...
Natural Log Function-Integration
9 mins 11th - Higher Ed CCSS: Adaptable
One of the strongest tools in integration is u-substitution, particularly when working with natural logs. In this step-by-step video presentation, a pleasant-voiced instructor walks through a number of integration problems. She begins...
The Second Fundamental Theorem of Calculus
2 mins 11th - Higher Ed
How many fundamental theorems are there? The Second Fundamental Theorem of Calculus is also known as the second part of the Fundamental Theorem of Calculus. Here's a video that introduces the theorem as the method to evaluate a definite...
Calculus - Early Transcendentals
9th - Higher Ed CCSS: Adaptable
This textbook takes the learner from the basic definition of slope through derivatives, integrals, and vector multivariable calculus. Each section is composed primarily of examples, with theoretical introductions and explanations in...
Volumes: Solids That are Not Solid of Revolution
3 mins 11th - Higher Ed
Viewers learn how to calculate the volume when the cross section is not a circle by using the same principle as if it was a circle. The video goes through an example of finding the volume of a figure where the cross sections are squares...
Nine Definite Integrals and Fundamental Theorem Of Calculus Problems
11th - Higher Ed
In this definite integral worksheet, student find the value of five definite integrals. Student then explain why a definite integral inequality holds true. Finally, students are given the graph of a functions and asked to determine...
What Does Area Have to Do with Slope? | Essence of Calculus, Chapter 9
13 mins 11th - Higher Ed
It seems like area and slope wouldn't have any connection. Here is a video that explains how to find the average value of a function over an interval. It connects the area under a curve to the slope of the antiderivative curve.
Exploration 4: Definite Integrals by Trapezoidal Rule
10th - 12th
In this integral learning exercise, learners geometrically estimate distance in given problems. They use the trapezoidal rule to determine definite integrals. Students explore distance and velocity. This three-page learning exercise...
I'm Lovin' It: Finding Area Between Curves
11th - Higher Ed CCSS: Designed
Students explore the concept of finding the area between two curves. In this finding the area between two curves lesson, students model the logos of McDonalds, Nike, and Motorola on grid paper. Students find functions to represent the...
Solving Differential Equations via the Fundamental Theorem of Calculus
11th - 12th
Students use their TI-89 calculator to compute derivatives and anti-derivatives. In this differential equation activity, students follow detailed directions to complete one table of derivative/anti-derivative values. They compute the...
Finding The Area Under a Curve Using Rectangles
16 mins 11th - Higher Ed
Here's an AP Calculus video that provides a discussion on determining an approximate for the area under a curve by calculating the sum of areas of rectangles that is smaller than the area and by finding the sum of areas of rectangles...
Separation of Variables and Initial Value Problem
5 mins 11th - Higher Ed
Ap Calculus classes learn how to solve a differential equation by getting like variables together with a video that presents an example of how to solve a differential equation by using the method of separation of variables. The example...
Approxiamte Solutions to Differential Equations-Slope Fields (graphical) and Euler's Method (numeric)
Twelfth graders explore differential equations. In this calculus lesson, 12th graders explore Euler’s Methods of solving differential equations. Students use the symbolic capacity of the TI-89 to compare Euler’s Method of numeric...
Lesson #100 The Fundamental Theorem of Calculus and Area Under the Curve
11th - 12th
Students explore the Fundamental Theorem of Calculus and apply the properties of definite integrals to solving equations. As a class, they explore formulas to use in evaluating integral yields in regions above and below the x-axis....
The Fundamental Theorem of Calculus and Properties of the Definite Integral
11th - Higher Ed
Students discuss the importance of fundamental theorems in math. In this calculus lesson, students define the fundamental theorem of calculus and discuss why it is so important they understand it. They work problems to model how this...
Integration By Parts and Quiz on Basic Integration Formulas
12th - Higher Ed
Students solve integrals using integration by parts. In this calculus lesson, students review problems using integration by parts, repeated integration by parts and constant integration. They take a Quiz after they solve review problems.
The Paradox of the Derivative | Essence of Calculus, Chapter 2
19 mins 11th - Higher Ed
It turns out that "instantaneous rate of change" isn't an accurate representation of the derivative. Viewers of the second video in a series of 11 learn about the concept of the derivative, from the limit of a difference quotient to the...
Visualizing the Chain Rule and Product Rule | Essence of Calculus, Chapter 4
17 mins 11th - Higher Ed
Take a look at the product rule and chain rule through the eyes of geometry. The fourth video in an 11-part series continues to explore derivative rules using geometry. An area model and a set of number lines help viewers understand the...
Implicit Differentiation, What's Going on Here? | Essence of Calculus, Chapter 6
16 mins 11th - Higher Ed
Teach implicit differentiation explicitly. An engaging video explains implicit differentiation to viewers. It describes how small changes in x and y can be thought of as contributing to the derivative dy/dx. This is the sixth video in a...