Integrals Teacher Resources

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...

Class members view how to derive the formula to integrate by parts with a video that uses the Product Rule from the beginning of AP Calculus to derive the rule to integrate products. The resource shows the formula in two different forms,...

Present examples of trigonometric integrals with a video that shows an example of determining a trigonometric integral. The AP Calculus example shows that many of the trigonometric integrals require manipulation and using trigonometric...

Demonstrate a complex integration by using partial fractions with an AP Calculus resource that works an example of integrating a rational function. The function's denominator has linear factors with one of them repeated. 

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

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,...

Learning about definite integrals is fundamental to any calculus course. The eighth of 16 parts in Unit 6 - Integration focuses on the Fundamental Theorem of Calculus. Scholars first see how to find antiderivatives, then discover how to...

Use the Fundamental Theorem of Calculus to find a derivative. With an example, pupils observe how being to derive a formula to help determine the derivative of any given integral. The video derives the formula using the first part of the...

The test is not all about skills. The six free-response questions contain two real-world application problems. Those items deal with populations and velocities. The other four questions ask pupils to show their knowledge of calculus...

Calculus classes definitely need to learn about indefinite integrals. Individuals watch an informative video to learn the antiderivative rules for exponential, logarithmic, trigonometric, and inverse trigonometric functions. To solidify...

What do a zoo, snow, and a moving particle have in common? The six free-response items from the 2010 AP® Calculus BC exam allow teachers and pupils see how items may show up in context. Three of the questions are from only the BC portion...

What's on the test? Released items provide insight into the AP Calculus test. The six items are split into two groups, two calculator items and four non-calculator items. Resources allow teachers to see what kinds of answers test takers...

So this is the real test? The resource provides the free-response questions from the 2011 AP Calculus AB exam. The six questions are split into two sections, calculator and non-calculator items. Several resources give teachers...

What is the important stuff? The free-response questions from the 2013 Calculus AB exam highlight the topics in calculus assessed that year. Items provide pupils the opportunity to experience questions similar to what they will see on...

Grow your knowledge of Calculus AB. Items released from the 2007 AP® Calculus AB exam provide information to teachers about the importance of particular topics. Pupils use the questions to gain an understanding of ways the exam assesses...

How much of the material is really important? Pupils use the free-response questions from the 2014 AP Calculus BC exam to see how the questions appear. With the supporting material, teachers understand the topics that appear on the test...

How will the topics be assessed? Using the six released items from the Calculus AB test, pupils see how the exam assesses content from the course. With the additional materials covering test taker's responses and scoring keys, teachers...

Give classes a sneak peek at an upcoming test. Scholars work released items from the AP Calculus AB test to prepare for their own exams. The resource consists of six items, two graphing calculator items, and four non-calculator items....

The split is 50-50. Released free-response questions from the 2016 AP Calculus BC show that half the questions are from the AB portion of the course and the others are from the BC portion. Teachers and pupils use the items to prepare and...

What was one of the big takeaways from 2009? By reviewing the released AP® Calculus free-response questions, pupils and teachers realize that performing mathematics is not all there is to doing well on the exam. Several items require...

How will the exam ask this question? The free-response questions from the 2015 AP Calculus BC exam demonstrate how questions appear on the test. Using the questions, pupils gain experience answering similar inquiries to what they see on...

Develop more than just a topical approach to the exam. The six free-response questions from 2006 reveal how the AP exam assesses topics. By using the questions, pupils practice topics such as velocity, sketch slope fields, solving...

Is this going to be on the test? The resource contains the AP Calculus AB free-response questions that were on the 2010 test. Pupils use the six questions to prepare for their tests. Teachers use the included response resources to...