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, I<br />
Problem<br />
Let F = Pi + Qj + Rk be a continuous vector field on R 3 which<br />
moves a particle along a smooth curve C. What is the work W<br />
done?<br />
Easy case<br />
If F is constant and moves the particle along a line segment<br />
from P to Q,<br />
W = F · D,<br />
where D = −→<br />
PQ is the displacement vector.
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