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 />
<strong>Line</strong> <strong>integrals</strong>, III<br />
Theorem<br />
For continuous f :<br />
�<br />
�<br />
� b<br />
�dx<br />
f (x, y) ds = f (x(t), y(t))<br />
dt<br />
C<br />
Important<br />
a<br />
� 2<br />
+<br />
� �2 dy<br />
dt.<br />
dt<br />
The value <strong>of</strong> the integral does not depend on the<br />
parametrization <strong>of</strong> C as long as C is traversed exactly once as<br />
t increases from a to b.