Is the same thing a line integral and a path integral?

I'm pretty sure the answer is "yes." Can you present the context?

a line integral is the integral of a vector field projected onto a path.

a path integral is the integral of a function along a path.

In my calculus III class, the integral along a path was called a line integral with no reference to fields. It was just the integration if some function of the appropriate number of variables from one point to another as the variables changed in the specified manner (such that they represented some path in the n-D space). I can't remember the name of the book, but I distinctly remember the words "Early Vectors" somewhere on the cover.

"Line integral" and "path integral" are different names for the same thing.

don t take my word for it.

<a href="http://mathworld.wolfram.com/PathIntegral.html">path integral</a>

<a href="http://mathworld.wolfram.com/LineIntegral.html">line integral</a>

mathworld is in agreement with my elementary calculus book (marsden and tromba),that there is a difference. (a line integral is a special type of path integral, according to this definition)

All I'm saying is that the context should be declared. Just because mathworld says one thing that agrees with a text book, that does not mean that these definitions agree with the usage in Lucas' case.

Originally posted by errandir
All I'm saying is that the context should be declared. Just because mathworld says one thing that agrees with a text book, that does not mean that these definitions agree with the usage in Lucas' case.

$5 says that the context is elementary vector calculus.

Well, I don't think I'll take that bet, because that's what I think, too. However, I also realize that the professor in question (assuming this is in the context of a lecture in elementary vector calculus) may have used the term "line integral" to refer to the thing that you are describing to be a "path integral."