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what does that sign mean? a integral sign with a circle on it.

- Thread starter PrudensOptimus
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- #1

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what does that sign mean? a integral sign with a circle on it.

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so this line integral is the same as a normal integral?

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A line integral is performed not over the entire domain of the integrand, but only over a one-dimensional subspace of the domain (a closed curve).Originally posted by PrudensOptimus

so this line integral is the same as a normal integral?

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Tom Mattson

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A "normal" integral need not be performed over the entire domain of the integrand, either.Originally posted by Ambitwistor

A line integral is performed not over the entire domain of the integrand, but only over a one-dimensional subspace of the domain (a closed curve).

By "normal integral" I take you to mean "integral along the x-axis".Originally posted by PrudensOptimus

so this line integral is the same as a normal integral?

A line integral is a generalization of a "normal integral". Line integration is what results when one realizes that the x-axis is not a "sacred path" in R

The so-called "normal integral"

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HallsofIvy

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A line integral is the integral of a function of 2 or more independent variables along a given path between 2 points in the domain of definition. You can write the one-dimensional path in terms of parametric equations in one parameter, write the function, restricted to that path, in terms of that parameter and integrate that in exactly the way you do "normal integrals" (of one variable).

Such a path does not HAVE TO BE closed. If it is, then you have the integral symbolized by the "integral sign with a circle on it".

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