Line integrals - University of Alberta
Line integrals - University of Alberta
Line integrals - University of Alberta
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MATH 209—<br />
Calculus,<br />
III<br />
Volker Runde<br />
<strong>Line</strong> <strong>integrals</strong><br />
in R 2<br />
Types <strong>of</strong> line<br />
<strong>integrals</strong><br />
<strong>Line</strong> <strong>integrals</strong><br />
in R 3<br />
<strong>Line</strong> <strong>integrals</strong><br />
<strong>of</strong> vector fields<br />
Properties <strong>of</strong> line <strong>integrals</strong><br />
Definition<br />
If C is any curve in R 2 , we write −C for the curve with<br />
reversed orientation.<br />
Properties<br />
We have �<br />
and �<br />
−C<br />
−C<br />
but �<br />
−C<br />
�<br />
f (x, y) dx = − f (x, y) dx<br />
C<br />
�<br />
f (x, y) dy = − f (x, y) dy,<br />
C<br />
�<br />
f (x, y) ds =<br />
C<br />
f (x, y) ds.
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