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Unformatted text preview: t x t r ≤ ≤ = , ) ( ), ( ) ( . If j N i M y x F + = ) , ( is conservative in R , and M and N are continuous in R , then ( 29 ( 29 ) ( ), ( ) ( ), ( a y a x f b y b x f r d f r d F C C-= • ∇ = • ∫ ∫ where f is a potential function of F. That is, ) , ( ) , ( y x f y x F ∇ = . Example: Use the Fundamental Theorem of Line Integrals to evaluate ∫ • C r d F where ( 29 ( 29 j xy i y y x F 2 1 ) , ( 2 + + = along the path from (0,0) to (2,0) as shown in the diagram. How cool is that?!...
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This note was uploaded on 01/13/2012 for the course MATH 2574 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.
- Spring '12