Greens Theorem for negatively orientated curve

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SUMMARY

Green's Theorem can be applied to negatively oriented curves by simply negating the result obtained from the integral calculated with positive orientation. The key takeaway is that the orientation of the path directly affects the sign of the integral, and this adjustment allows for the use of Green's Theorem without any complications. Thus, when dealing with negative orientation, one can effectively 'pretend' the path is positively oriented and then invert the sign of the result.

PREREQUISITES
  • Understanding of Green's Theorem in vector calculus
  • Knowledge of path integrals and their properties
  • Familiarity with the concept of curve orientation
  • Basic proficiency in vector calculus terminology
NEXT STEPS
  • Study the implications of curve orientation on line integrals
  • Explore advanced applications of Green's Theorem in physics
  • Learn about Stokes' Theorem and its relationship to Green's Theorem
  • Investigate examples of path integrals with varying orientations
USEFUL FOR

Students and professionals in mathematics, particularly those studying vector calculus, as well as educators teaching Green's Theorem and its applications in various fields.

thrillhouse86
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Hey All,

in vector calculus we learned that greens theorem can be used to solve path integrals which have positive orientation. Can you use greens theorem if you have negative orientation by 'pretending' your path has positive orientated and then just negating your answer ?

Regards,
THrillhouse
 
Physics news on Phys.org
yes, the only change "negative orientation" instead of "positive orientation" makes on the integral is a change in sign. If you allow for that, there is no problem.
 

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