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, XV<br />
Example (continued)<br />
Parametrize C2:<br />
Thus:<br />
All in all:<br />
x = 3, y = 4, z = 5 − 5t, t ∈ [0, 1].<br />
�<br />
C2<br />
�<br />
y dx + z dy + x dz = −15<br />
C<br />
y dx + z dy + x dz = 49<br />
2<br />
� 1<br />
0<br />
dt = −15.<br />
− 15 = 19<br />
2 .
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