Opinion? Solids of Revolution/Integration Techniques

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Homework Help Overview

The discussion revolves around applying concepts of solids of revolution and integration techniques in a calculus context. The original poster is exploring whether a specific equation related to a solid of revolution can be solved using integration techniques such as integration by parts, substitution, or partial fractions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions the applicability of integration by parts to their chosen problem. Other participants suggest alternative methods and express uncertainty about the effectiveness of various integration techniques.

Discussion Status

The discussion is ongoing, with participants providing insights and suggestions regarding the integration techniques. There is a recognition of the challenges associated with the chosen problem, and the original poster is considering alternative problems, such as those involving arc lengths.

Contextual Notes

Participants are discussing the constraints of the problem, including the requirement to use specific integration techniques and the possibility of selecting different types of problems, such as arc lengths.

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Homework Statement



Hey everyone. In my calc course I need to create (or find on the web) a problem and apply the below two concepts that I learned in the class.

Concepts:
Solids of Revolution.
Integration Techniques: Parts, Substitution, or Partial Fractions.

Homework Equations



The problem I chose was:

http://curvebank.calstatela.edu/volrev/vase7.gif

The Attempt at a Solution



Well, the question I am asking is basically if this equation I found can be solved using one of the Integration Techniques. I was thinking Parts. Would that be right?
 
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Just expand it out. Then use the double angle formula for cos2x, to replace sin2x
 
So One of the Integration Techniques can't be used, then?
 
Integration by parts might make it more complex, substitution, I don't think will work and you can't split it into partial fractions.
 
Well, cruds.

Thank you! I'm off to find another problem then I guess. They did say I could also choose arc lengths. Maybe I'll go with that...
 

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