15_R_8 - F = ( x 2 y + 3 xyz + y 3 z ) . Thus Z F • d r =...

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8. R F d r can be determined using only the endpoints of , provided F = ( axy + 3 yz ) i + ( x 2 + 3 xz + by 2 z ) j + ( bxy + cy 3 ) k is conservative, that is, if ax + 3 z = F 1 y = F 2 x = 2 x + 3 z 3 y = F 1 z = F 3 x = by 3 x + by 2 = F 2 z = F 3 y = bx + 3 cy 2 . Thus we need a = 2, b = 3, and c = 1. With these values,
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Unformatted text preview: F = ( x 2 y + 3 xyz + y 3 z ) . Thus Z F • d r = ( x 2 y + 3 xyz + y 3 z ) ± ± ± ± ( 2 , 1 , 1 ,) ( , 1 ,-1 ) = 11-(-1 ) = 12 ....
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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