Calculating Line Integral from Potential Function of Vector F

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Homework Help Overview

The discussion revolves around the calculation of a line integral using a potential function of a vector field. Participants are exploring the relationship between potential functions and line integrals in vector calculus.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions whether a line integral can be calculated from a potential function. Some participants affirm this and discuss the relationship between the potential function and the endpoints of the integral.

Discussion Status

The discussion includes affirmations of the original poster's understanding, with some participants providing insights into the path independence of line integrals in the context of potential functions. There appears to be a productive exchange of ideas regarding the implications of having a potential function.

Contextual Notes

No specific constraints or missing information have been noted in the discussion.

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Homework Statement



If I know the potential function if a vector F can I calculate the line integral from point A to B using that potential function?

Homework Equations





The Attempt at a Solution

 
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Absolutely.
 
just based on my understanding if I have the potential function then the line integral is just g(Q) - g(A). Where A is the starting point of the curve and Q is the ending point.. g is the potential function.. correct?
 
Right again. The line integral is path independent if the vector field has a potential.
 

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