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> in R 3 , II<br />
As in R 2 . . . (continued)<br />
and. . .<br />
�<br />
P(x, y, z) dx + Q(x, y, z) dy + R(x, y, z) dz<br />
C<br />
� b<br />
= P(x(t), y(t), z(t))x ′ (t) dt<br />
a<br />
� b<br />
+ Q(x(t), y(t), z(t))y ′ (t) dt<br />
a<br />
� b<br />
+ R(x(t), y(t), z(t))z<br />
a<br />
′ (t) dt.
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