Green's Theorem not working in this problem HELP

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Homework Help Overview

The discussion revolves around a problem related to line integrals and the application of Green's Theorem. The original poster expresses difficulty in applying the theorem to their specific problem, which involves vector fields and potential functions.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the implications of the hint provided regarding vector fields and potential functions. There are questions about the meaning of certain statements and the validity of using Green's Theorem in this context. Some participants suggest considering direct integration methods instead.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants have offered insights into the nature of conservative fields and the implications for the problem at hand. There is no explicit consensus, but guidance has been provided regarding potential approaches.

Contextual Notes

There is mention of the original poster's uncertainty about how to approach the problem, as well as the specific conditions under which Green's Theorem may not apply. The discussion also touches on the need for parameterization in the context of integrating around a circle.

unilquer
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I have a problem from line integrals.
My question is attached as a jpeg.
Green's theorem is not valid for mine and i couldnot find a way.
Pls take care of it.
 

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Should you show your attempt?
 
What does the last sentence mean?
Suppose you have the task of providing such vector fields on demand
 
It is just a clue. It goes on with saying this kind of functions can be created without much effort and asks how they are written.
And unfortunately i don't have much idea how to approach the problem.
 
I would say that the hint given is a big one indeed. It would save you a lot of computational effort if you understood it correctly. Have you learned about potential functions and conservative vector fields yet?
 
Actually, i predicted that but could not be sure. Than the answer is 0 since this is a conservative field and surface is a complete circle right?
 
Since Green's theorem does not work here, then you need to directly integrate around the circle. What parameterization can you use for a circle about the origin with radius r?
 
Yep, that should be it. Although it's more correct to say it's a line integral over a closed curve.
 

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