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, XVII<br />
Example (continued)<br />
Thus:<br />
�<br />
W =<br />
=<br />
C<br />
� 2<br />
−1<br />
F · dr =<br />
� 2<br />
−1<br />
(t sin(t 2 )i + t 2 j) · (i + 2tj) dt<br />
t sin(t 2 ) + 2t 3 dt = 1<br />
2<br />
cos u<br />
�<br />
�<br />
= − �<br />
2<br />
u=4<br />
+<br />
u=1<br />
15<br />
2<br />
� 4<br />
1<br />
sin u du + t4<br />
2<br />
�<br />
�<br />
�<br />
�<br />
t=2<br />
t=−1<br />
1<br />
= (15 − cos 4 + cos 1).<br />
2
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