Path integral and line integrals

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Path integrals and line integrals are often used interchangeably but have distinct meanings. A line integral typically integrates a vector function along a curve, while a path integral, particularly in quantum mechanics, sums over all possible paths. Both integrals consider the function along a curve with respect to arc length, making them independent of parameterization. The confusion arises from their overlapping uses in different contexts. Understanding these differences is crucial for applying the correct concept in mathematical and physical problems.
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Homework Statement



what is the difference between path integral and line integral?

Homework Equations



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The Attempt at a Solution



is path integral over a scalar function

and line integral is over vector function?


I'm confused about this pls help me understand

thanks in advance
BA
 
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they can quite often be used to refer to the same thing, see
http://en.wikipedia.org/wiki/Line_integral

they basically integrate the function along the curve with repsect to arc length

as the integral is with repsect to arc length it is independent of parameterisation

also different is the path integral in quantum mechanics which is a sum over all possible paths
 

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