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> <strong>of</strong> vector fields, VI<br />
Definition<br />
Let F = Pi + Qj + Rk be a continuous vector field on R 3 , and<br />
let C be a smooth curve given by the vector function r(t) for<br />
t ∈ [a, b]. The line integral <strong>of</strong> F along C is<br />
�<br />
C<br />
� b<br />
F · dr = F(r(t)) · r<br />
a<br />
′ (t) dt<br />
�<br />
= P(x, y, z) dx + Q(x, y, z) dy + R(x, y, z) dz.<br />
C
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