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 />
Examples, VI<br />
Example<br />
Evaluate �<br />
(−5, −3) to (0, 2).<br />
Parametrize the curve as<br />
C y 2 dx + x dy where C is the line segment from<br />
r(t) = 〈−5, −3〉 + t(〈0, 2〉 − 〈−5, −3〉) = 〈−5 + 5t, −3 + 5t〉,<br />
so that<br />
x = −5 + 5t, y = −3 + 5t, t ∈ [0, 1].
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