# Integration and Area Teacher Resources

Find Integration and Area lesson plans and worksheets
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#### AP Calculus AB

For Students 11th - 12th
Prepare high school mathematicians for the AP Calculus AB exam with a collection of 38 videos that can be used to introduce the topics or as a review. The videos focus on two processes; differentiating a function and integrating a...
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#### AP Calculus AB Unit 6: Integration and Accumulation of Change

For Teachers 11th - 12th
The 14 lessons in the AP Calculus AB Unit 6: Integration and Accumulation of Change use informative videos to introduce the topic of each lesson and model procedures. Each resource packet includes a video, worksheets, practice solutions,...
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#### Math Handbook: Calculus

For Students 10th - 12th
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...
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#### Introduction to Calculus

For Teachers 11th - Higher Ed Standards
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,...
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#### Historical Reflections on the Fundamental Theorem Of (Integral) Calculus

For Teachers 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...
7:43
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#### Calculus, What Is It Good For?

For Students 11th - Higher Ed
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...
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#### The Fundamental Theorems of Calculus

For Teachers 11th - Higher Ed
Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The...
5:38
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#### Approximating Area Using Rectangles

For Students 11th - Higher Ed
Finding area using rectangles—isn't that a little too simplistic for a calculus course? Viewers learn how to approximate area under a curve using rectangles in the first installment of a seven-part video series on the definite integral....
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#### Fundamental Theorem of Calculus

For Teachers 10th - 12th
Does it make more sense to teach the Second Fundamental Theorem of Calculus before the First Fundamental Theorem of Calculus? An AP® Calculus curriculum module explores the interesting question. A set of five worksheets first looks at...
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#### Properties of Definite Integrals

For Students 11th - Higher Ed
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....
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#### Trapezoidal and Midpoint Approximations: Area of a Skirt

For Students 11th - Higher Ed
When are trapezoids better than rectangles? Using trapezoids pupils approximate the area of fabric defined by a function. Just like with rectangles, learners realize the more trapezoids the more accurate the approximation. Scholars use...
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#### 2017 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
Pupils use the six released free-response questions from an AP Calculus BC exam to prepare for their own exam. The questions cover a range of topics from the BC curriculum, with half of the items coming strictly from AB material and the...
17:05
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#### Essence of Calculus, Chapter 1

For Students 11th - Higher Ed
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...
1 In 1 Collection 16:11
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#### Finding The Area Under a Curve Using Rectangles

For Students 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...
20:46
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#### Integration and the Fundamental Theorem of Calculus | Essence of Calculus, Chapter 8

For Students 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...
1 In 1 Collection 8:18
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#### Areas Between Curves

For Students 11th - Higher Ed
There are times that it is necessary to add areas to find the area between the curves. The video for AP Calculus presents how to find the area between curves by subtracting the area under the lower curve from the area under the upper...
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#### 2002 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
Become better at the test concepts. An educational resource presents six free-response questions from the AP® Calculus AB exam. Pupils use the items to practice the content, which contains concepts ranging from particle motion to ships...
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#### Area and Volume

For Students 11th - Higher Ed
An AP calculus lesson begins with an activity to determine the volume of a solid using a cross-section. Next, learners review the ways to find the area between two curves , as well how to find the volume of a solid created from the...
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#### Discovering a Fundamental Fact about Integration

For Teachers 11th - 12th
Sketch on coordinate axes to find the exact value of an integral shown. Individuals complete the data grid with the values of integrals returned and use inductive reasoning to guess the formula.
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#### Sum of Rectangle Areas to Approximate Integrals

For Teachers 11th - 12th
Students explore the concept of approximating integrals.  In this approximating integrals lesson plan, students approximate integrals by finding the area of rectangles.  Students use a graphing calculator to find the left, right, and...
1 In 1 Collection
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#### Calculus AB/BC - The Fundamental Theorem of Calculus and Definite Integrals

For Students 10th - 12th
New ReviewLearning 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...
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#### 2004 AP® Calculus AB Free-Response Questions Form B

For Students 10th - 12th
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...
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#### 2010 AP® Calculus BC Free-Response Questions

For Students 10th - 12th
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...
5:56
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#### Integrals - Calculus

For Students 11th - Higher Ed
Introduce the opposite of differentiation. Pupils learn the basic definition of integration and how to integrate a polynomial. The video shows learners how the integral is the opposite of the derivative. Individuals see how to confirm...