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

[jgens]

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 (t_i - t_i-1) appears in the denominator when it should not. Thanks!

 

[jgens]

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.

 

[jgens]

No one has any comments?

 

[Firepanda]

Just so you know that you're not waiting because no one wants to help you, your attachments are

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