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 />
Types <strong>of</strong> line <strong>integrals</strong>, I<br />
More line <strong>integrals</strong><br />
We call �<br />
C f (x, y) ds the line integral with respect to arclength.<br />
Suppose that C is given by the parametric equations<br />
Then<br />
so that<br />
x = x(t), y = y(t), t ∈ [a, b].<br />
dx<br />
dt = x ′ (t) and<br />
dy<br />
dt = y ′ (t),<br />
dx = x ′ (t) dt and dy = y ′ (t) dt.
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