Integrals Teacher Resources

This heady calculus text covers the subjects of differential and integral calculus with rigorous detail, culminating in a chapter of physics and engineering applications. A particular emphasis on classic proof meshes with modern graphs,...

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...

Are your calculus pupils aware that they are standing on the shoulders of giants? This activity provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The...

If only there was a reference that listed all the formulas covered in calculus. Luckily, there is. This comprehensive 197-page handbook provides formulas and explanations for all topics in AP Calculus or in a standard college calculus...

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...

Explore the meaning of differentiation and integration. A video lesson describes in detail what differentiating and integrating an equation means using the momentum and kinetic energy formulas. Progressing from a linear to a quadratic...

Are you always looking for extra problem resources to incorporate in your classes?  A set of problems for a full AP Calculus course may be all you need! Each unit has a full set of questions and a sample test.

The inverse of matter is anti-matter, so the inverse of a derivative is an antiderivative. The lesson introduces antiderivatives and indefinite integrals to the class along with the notation for integrals. Groups work together to find...

Your calculus learners will enjoy this handy reference sheet containing the most used derivative and integral formulas.

Close your eyes and visualize a definite integral. An interactive provides a visualization of a function and definite integral on a closed interval. Pupils move one point of the interval in either the positive or negative direction....

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,...

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...

The concept of solving integrals by substitution with trigonometric functions is modeled by a video designed for AP Calculus classes. The narrator works an example problem using substitution and shows that careful substitution makes...

Dive into the essence of calculus. The first installment of an 11-part playlist introduces the video series by looking at the area of a circle and the area under curves. The narrator explains how to look at calculus as taking a hard...

Practice in the mechanics of using substitution in integration is often hard to come by in enough quantity for learners to really wrap their heads around the nuances of the technique. This worksheet set with solution key and worked...

From derivatives to antiderivatives and back again. Building on the second instructional activity of the three-part series covering functions, learners explore the concept of an antiderivative. They connect the concept to the graph of...

Looking for help in introducing integration by substitution to your calculus students?  Here is a lesson that walks a learner through a review of the change rule, and then by starting with more recognizable derivatives, it helps them...

Everything you wanted to know about calculus—and more! The resource is a complete Calculus textbook with explanations, examples, and practice problems. 

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...

Students explore the concept of definite integrals.  In this definite integrals lesson, students find the area between two curves.  Students use the Ti-Nspire to find the definite integrals of curves such as sine and cosine.

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...

In this A.P. Calculus worksheet, students complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields.  Some of the problems are multiple choice, while others are...

For this calculus worksheet, students evaluate given integrals. Problems contain exponents, square roots, and complex fractions. This two-page worksheet contains 16 multi-step problems. Answers are provided on page two.

Learners investigate the intervals represented by a function in this calculus lesson plan. They decide what interval of the function will be positive, negative or zero. They are then given graphs of functions and asked to analyze it.