Calculus 2 Find the volume problem

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Homework Help Overview

The problem involves finding the volume of a solid of revolution generated by rotating the area bounded by the curves y=x, y=0, x=2, and x=4 about the line x=1. The subject area is calculus, specifically focusing on methods for calculating volumes of solids of revolution.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss different methods for calculating the volume, including the washer method and cylindrical shells. There are attempts to verify calculations and explore the implications of using different methods.

Discussion Status

Several participants have shared their calculations, with some expressing uncertainty about their results. There is a mix of approaches being considered, and while some participants have indicated they have arrived at answers, there is no explicit consensus on the correctness of the solutions presented.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can share or the methods they can use. There is an ongoing discussion about the appropriateness of different methods for this specific problem.

hvidales
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Homework Statement



Find the volume: y=x, y=0, x=2, x=4; about x=1

Homework Equations



Washer method V= ∏∫ (R)^(2)-(r)^(2) dy

The Attempt at a Solution


0 to 4 is my a to b**

∏∫(from 0 to 4) of (1-4)^(2)-(1-y)^(2) dy

∏∫(from 0 to 4) of 9-(1-2y+y^(2)) dy

∏∫(from 0 to 4) of 8 + 2y - y^(2) dy

∏[8y+y^(2)-y^(3)/3](from 0 to 4)

∏[32+16-64/3]=80∏/3


That is my answer but I want to make sure that I got it correct. Thanks in advance!
 
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Hey people. So I reworked it and i got 76pi/3. Is this correct?
 
I got 24∏. With rotations about the x-axis it is usually easier to use cylindrical shells. It's much harder with washers, I don't even want to think about what you'd do for that. With cylindrical shells the integral would be from 0 to 4 of 2∏∫(x-1)x dx.
 
Hey I ended up getting it. Thanks for taking the time to work it out. :smile:
 

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