Line integrals - University of Alberta
Line integrals - University of Alberta
Line integrals - University of Alberta
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
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, X<br />
Example<br />
Evaluate �<br />
from (0, 2) to (−5, −3).<br />
Parametrize the curve as<br />
so that<br />
C y 2 dx + x dy where C is the line segment from<br />
r(t) = 〈0, 2〉 + t(〈−5, −3〉 − 〈0, 2〉) = 〈−5t, 2 − 5t〉,<br />
x = −5t, y = −5t + 2, t ∈ [0, 1].
Change language