Finding the Area Bounded by a Polar Curve: A Proof of Integrability Criteria

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Homework Help Overview

The original poster attempts to determine the expression for the area bounded by a polar curve and the criteria for integrability using both Darboux and Riemann sums. The context involves understanding proofs related to integrability in the realm of polar coordinates.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster seeks suggestions for correcting errors in their proof, particularly regarding the criterion for Riemann integrability. They express a desire for constructive criticism and mention issues with equation formatting due to file conversion.

Discussion Status

The discussion appears to be in its early stages, with the original poster awaiting feedback on their proof. There is a lack of responses, indicating that participants may still be considering the problem or awaiting further clarification.

Contextual Notes

The original poster notes that the conversion of their document to PDF has introduced errors in the equations, which may affect the clarity of their proof. Additionally, there is mention of attachments pending approval, which may limit the information available for review.

jgens
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Homework Statement



Determine the expression for the area bounded by a polar curve and the criterion for integrability using both Darboux and Riemann sums.

Homework Equations



N/A

The Attempt at a Solution



Any suggestions on how to correct any errors in the following proof, particularly in the steps determining the criterion for Riemann integrability are much appreciated. I'm not particularly great at proofs so constructive criticism is welcome. I had to convert the file to a pdf and it screwed up a couple of the equations, most notably, a factor of (ti - ti-1) appears in the denominator when it should not. Thanks!
 

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I found a better method to convert the file to a pdf. Hopefully this will make it easier to read and correct some of the conversion errors from the other pdf.
 

Attachments

No one has any comments?
 
Just so you know that you're not waiting because no one wants to help you, your attachments are

'Attachments Pending Approval'
 

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