Vector Calculus I 2022
This small group activity is designed to help students visual the process of chopping, adding, and multiplying in single integrals.
Students work in small groups to determine the volume of a cylinder in as many ways as possible.
The whole class wrap-up discussion emphasizes the equivalence of different ways of chopping the cylinder.
What students learn
Encourages students to think of several ways to solve the same problem.
Encourages students to think about different ways of chopping and adding.
Leads into The Cone.
A cylinder has circular base of radius \(R\) and height \(H\), both measured in
feet.
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What is the volume of the cylinder?
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Write down as many different integrals as you can for computing this volume.
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Do at least two of these integrals.
For some integrals, you may wish to use the fact that
\[\cos(2\alpha)=2\cos^2\!\alpha-1=1-2\sin^2\!\alpha\]
- Keywords
- Learning Outcomes
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