Volumes of Revolution
Emily Davis
5 min read
Study Guide Overview
This study guide covers calculating the volume of revolution around the y-axis using the disc method. It explains how to rewrite functions in terms of y, set up and evaluate the definite integral involving the rewritten function, and determine the boundaries of integration. The guide includes a worked example, practice questions, exam tips, and a glossary of key terms like solid of revolution.
#Volume with Disc Method Revolving Around the y-axis
#Table of Contents
- Introduction to Volume of Revolution Around the y-axis
- Disc Method for Calculating Volume
- Exam Tips
- Worked Example
- Practice Questions
- Glossary
- Summary and Key Takeaways
#Introduction to Volume of Revolution Around the y-axis
A volume of revolution around the y-axis is similar to a volume of revolution around the x-axis. It involves rotating an area bounded by a function and other boundary equations around the y-axis to form a solid shape. This shape's volume is what we are interested in calculating.
A solid of revolution is formed when an area bounded by a function and other boundary equations is rotated radians (360°) around the y-axis.
#Disc Method for Calculating Volume
To calculate the volume of revolution around the y-axis using the disc method, follow these steps:
- Identify the boundaries: Determine the re...
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