Volume Calculation Using Cylindrical Shells

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The discussion focuses on calculating the volume of a solid formed by rotating the region between the curves x = 3 + (y-2)² and x = 4 about the x-axis using cylindrical shells. The volume is expressed as an integral, specifically V = integral from 0 to 3 of ((4 - (y² - 4y + 7))(y + 1) dy), where the terms represent the height and radius of the cylindrical shell. Clarification was sought regarding the notation "(y-2)**2," which was confirmed to be equivalent to (y-2)². The original poster eventually resolved the problem independently. The thread highlights the importance of understanding cylindrical shell integration for volume calculations.
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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
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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