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 />
Examples, II<br />
Example<br />
Let C be the line segment from (0, 0) to (1, 1).<br />
Evaluate �<br />
C xy ds.<br />
Set<br />
x = t, y = t, t ∈ [0, 1].<br />
Then:<br />
�<br />
C<br />
xy ds =<br />
� 1<br />
0<br />
t 2√ 1 + 1 dt = √ 2<br />
� 1<br />
0<br />
t 2 dt =<br />
√ 2<br />
3 .