Green Theorem: Solving ∫(y+x^2*cosx)dx+(2x-y^2*sin(y))dy on x^2+y^2=1

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Discussion Overview

The discussion revolves around the application of Green's Theorem to evaluate the line integral ∫(y+x^2*cosx)dx+(2x-y^2*sin(y))dy over the boundary of the circle defined by x^2+y^2=1. Participants explore the correctness of the solution and the reasoning behind it.

Discussion Character

  • Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant expresses uncertainty about their solution to the integral, questioning if it is correct.
  • Another participant states that the answer obtained is 2π.
  • A third participant affirms the correctness of the answer, suggesting that it is a straightforward application of Green's Theorem.
  • A fourth participant expresses gratitude and indicates that the confirmed answer aligns with their expectations.

Areas of Agreement / Disagreement

There appears to be general agreement on the correctness of the answer being 2π, but the initial uncertainty expressed by one participant indicates that not all aspects of the discussion are settled.

Contextual Notes

Participants do not elaborate on the specific steps taken to arrive at the solution, leaving some assumptions and mathematical details unresolved.

Who May Find This Useful

Students or individuals interested in applying Green's Theorem in calculus, particularly in evaluating line integrals over closed curves.

Brunno
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Hello fellows,

I am not sure if the answer i got this question is the correct one. Could it not be it?

∫(y+x^2*cosx)dx+(2x-y^2*sin(y))dy within the llimit of the circle x^2+y^2=1
 
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Ah and the answer i got was 2pi
 
Yes, that is correct. Why would you be not sure? It's about as easy a Greens theorem problem as you can have!
 
Thank you man. That was the answer I was expecting to read too.
 

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