Volume Calculation Using Cylindrical Shells

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    Cylindrical Volumes
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Homework Help Overview

The discussion revolves around calculating the volume of a solid formed by rotating a region bounded by the curves x = 3 + (y-2)² and x = 4 about the x-axis, using the method of cylindrical shells.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to set up the integral for volume calculation but seeks confirmation on the correctness of their setup. Another participant questions the notation used in the original poster's expression.

Discussion Status

The discussion includes attempts to clarify notation and confirm the setup of the problem. One participant indicates they have resolved their issue independently, suggesting a potential conclusion to their inquiry.

Contextual Notes

There is a mention of notation that may have caused confusion, and the original poster expresses a willingness to clarify their setup if needed.

quickclick330
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Consider the given curves to do the following.
x = 3 + (y-2)**2, x = 4
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.


V = ??

****************

I set up the problem like this...

V = integral from 0 to 3((4-(y^2-4y+7))(y + 1) dy)


(height) (radius) ...of "shell"

Did I set this up right? Hopefully this is clear enough, if you can't understand I can clarify. Thanks for the help in advance!
 
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What does "(y-2)**2" mean? Did you mean (y-2)^2?
 
yes, sorry, it copy-pasted like that
 
never mind, i solved it finally
 

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