Line Integrals and Potentials
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The line integral depends on path
Equations are omitted for technical reasons - download the original pdf
The following example illustrates the observation that if a vector function is integrated along a different path, the endpoints being the same, then in general the value of the line integral will not be the same. So, even when the endpoints are the same, the line integral depends on the path between them. Example (3) [Example goes here - download the original pdf to see it.]
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Contents of
Line Integrals and Potentials
1 Line integrals that are independent of path
2 Curve of integration
3 Line integrals
4 Potentials
5 Proof of the theorem
6 The line integral depends on path
7 Potentials and integration around a closed curve
8 The line integral does not depend on the parameter
9 Conservative scalar fields
10 Work integral
11 Work done is equal to gain in kinetic energy
12 Exact differential forms
13 Simply connected domains
14 Exactness and independence of path
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