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Unformatted text preview: integrals: Remark 2.5.4. The path integral of a function over a parametrized curve is unchanged by reparametrization; when the parametrization −→ p : R → R 3 is regular, we have i C f d s = i b a f ( −→ p ( t )) v v v ˙ −→ p ( t ) v v v dt. As two examples, let us take C to be the parabola y = x 2 between (0 , 0) and (1 , 1), and compute the two integrals i C xd s i C y d s . To compute the Frst integral, we use the standard parametrization in terms of x −→ p ( x ) = ( x,x 2 ) , ≤ x ≤ 1;...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08