# Integration and Volume Teacher Resources

Find Integration and Volume lesson plans and worksheets
Showing 1 - 24 of 90 resources
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#### Volumes by Cylindrical Shells

For Students 11th - Higher Ed
Shells sometimes work better than washers. The AP Calculus video presents an example of finding the volume of a rotational solid by using the shell method. The method uses the integral of the lateral surface area of a cylinder as opposed...
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#### Volume by Cross Sections

For Teachers 11th - 12th
Eleventh and twelfth graders find the volume of figures using cross sections. They use their Ti-Nspire to find the volume of a solid formed by cross sections of a function. Pupils find the integrals of the shapes using cross sections.
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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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#### Volume by Disks: The Vase Case

For Students 11th - Higher Ed
Finding the volume is an integral characteristic of a vase. Using the idea that summing the areas of cross-sectional disks will calculate the volume of a rotational solid, pupils find the volume of a vase. Scholars determine the interval...
7:54
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#### Properties of the Definite Integral

For Students 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...
3:23
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#### Volumes: Solids That are Not Solid of Revolution

For Students 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...
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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...
2:54
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#### Solving Integrals Using Substitution

For Students 11th - Higher Ed
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...
7:38
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#### Volumes by Washers

For Students 11th - Higher Ed
Here's an AP Calculus resource that works an example problem of finding the volume where the cross sections of a solid are washer shaped. In the example the axis of rotation is vertical, creating horizontal washers.
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#### Volume by Cross Section: Volume of the Cone

For Students 11th - Higher Ed
Discover another way to find the volume of a cone. Pupils explore how the area of a cross section changes as it moves through a cone. The interactive uses that knowledge to develop the integral to use to find the volume of the cone....
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#### The Second Fundamental Theorem of Calculus

For Students 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...
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#### Calculus Volume 1

For Students 11th - Higher Ed
Differentiate between calculus concepts. The beginning of a helpful calculus resource begins with a short review of functions and moves right into limits to define derivatives. The six-chapter resource continues with applications of...
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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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#### Trigonometric Integrals

For Students 11th - Higher Ed
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...
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#### AP Calculus Practice Exam

For Students 11th - 12th
In this Calculus worksheet, students are provided with problems of a similar nature to those on their exam.  Problems include limits, derivatives, and integrals.  The four page worksheet contains twenty-eight problems.  Answers are not...
8:48
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#### Volumes by Slicing

For Students 11th - Higher Ed
Find the volume of a rotational solid by integrating the area of a slice. The AP Calculus resource works through an example of finding the volume of a solid created by rotating a function about the x-axis. The presentation breaks the...
5:41
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#### Integration by Parts

For Students 11th - Higher Ed
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,...
10:30
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#### Integration by Partial Fractions

For Students 11th - Higher Ed
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.
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#### Calculus Volume 3

For Students 11th - Higher Ed
See calculus to the end. The eBook is the last of a three-volume series covering college-level calculus topics. Scholars begin with parametric equations and polar coordinates before moving to vectors, finally ending with multi-variable...
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#### AP Calculus Practice Exam

For Students 11th - 12th
In this practice exam learning exercise, students solve 17 multiple choice problems. Students find derivatives, points of continuity, maximums, minimums, integrals, and area of enclosed regions.
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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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#### 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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#### Average Value of a Function

For Students 11th - Higher Ed
Viewers learn how to find the average of a variable density with a video made for AP Calculus. The presenter applies the formula to find the average value of a function with an example that provides a density function for a rod. The...
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#### AP Calculus Practice Exam

For Students 11th - 12th
In this Calculus worksheet, learners are provided with practice problems for their exam.  Topics covered include derivatives, area bounded by a curve, local maximum, instantaneous rate of change, and the volume of a solid of revolution. ...