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Unformatted text preview: d r = Z C r f d r = f (1 ; 1) & f (0 ; 0) = & 32 & 0 = & 32 . Now we show how to do the integral using the denition of line integrals: The curve C can be parameterized as r ( t ) = t i + t 2 j t 1 from which we see that r ( t ) = i + 2 t j and F ( r ( t )) r ( t ) = ( & 32 j ) ( i + 2 t j ) = & 64 t . Thus Z C F d r = Z C F ( r ( t )) r ( t ) dt = Z 1 & 64 t dt = & 32 . 1...
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 Fall '10
 Ellermeyer
 Math

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