15_R_10 - = -3-e + 3 t 2 ± ± ± 1 = -e .

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10. a) F = ( 1 + x ) e x + y i + ( xe x + y + 2 y ) j - 2 z k = ( xe x + y + y 2 - z 2 ). Thus F is conservative. b) G = ( 1 + x ) e x + y i + ( xe x + y + 2 z ) j - 2 y k = F + 2 ( z - y )( j + k ). : r = ( 1 - t ) e t i + t j + 2 t k , ( 0 t 1 ) . r ( 0 ) = ( 1 , 0 , 0 ), r ( 1 ) = ( 0 , 1 , 2 ) . Thus Z G d r = Z F d r + Z 2 ( z - y )( j + k ) d r = ( xe x + y + y 2 - z 2 ) ± ± ± ( 0 , 1 , 2 ) ( 1 , 0 , 0 ) + 2 Z 1 0 ( 2 t - t )( 1 + 2 ) dt
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Unformatted text preview: = -3-e + 3 t 2 ± ± ± 1 = -e ....
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