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>, II<br />
The construction<br />
Divide [a, b] into n subintervals [tj−1, tj].<br />
Set xj = x(tj) and yj = y(tj). The corresponding points<br />
Pj(xj, yj) divide C into n subcurves with lengths ∆s1, . . . , ∆sn.<br />
) on each subcurve.<br />
Pick a support point Pj(x ∗ j<br />
Definition<br />
, y ∗<br />
j<br />
The line integral <strong>of</strong> f along C is defined as<br />
�<br />
C<br />
f (x, y) ds = lim<br />
n→∞<br />
n�<br />
j=1<br />
f (x ∗ j , y ∗<br />
j )∆sj.