Calculating Line Integral from Potential Function of Vector F

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If a potential function for a vector field F is known, the line integral from point A to point B can be calculated using the formula g(B) - g(A), where g represents the potential function. The calculation is valid because the line integral is path independent in vector fields that possess a potential function. This means that the integral's value depends only on the endpoints, not the specific path taken. Therefore, confirming the understanding that the potential function simplifies the computation of line integrals in such cases is accurate. The discussion emphasizes the relationship between potential functions and line integrals in vector fields.
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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?

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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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