Volumes of Revolution
Emily Davis
5 min read
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Study Guide Overview
This study guide covers calculating the volume of revolution around the x-axis using the disc method. It explains the formula V = π∫ab[f(x)]² dx and provides a worked example, practice questions, exam tips, and a glossary of key terms like solid of revolution, region, and definite integral.
#Volume with Disc Method Revolving Around the x-axis
#Table of Contents
- Introduction to Volume of Revolution
- Using the Disc Method
- Exam Tips
- Worked Example
- Practice Questions
- Summary and Key Takeaways
- Glossary
#Introduction to Volume of Revolution
#What is a Volume of Revolution Around the x-axis?
A solid of revolution is formed when an area bounded by a function (and other boundary equations) is rotated 2\pi radians (360°) around the -axis. The volume of revolution is the volume of this solid.
#Using the Disc Method
#How to Calculate a Volume of Revolution Around the x-axis?
For a continuous function , if the region bounded by:
- the curve and the -axis
- between and
is rotated 2\pi radians (360°) around the -axis, then the volume of revolution is:
V = \pi \int_...
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