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Unformatted text preview: F ). Page 3 of 4 6. (10 points each) Evaluate each of the following line integrals: (a) ds z x C ∫ + ) 9 2 ( where C is parameterized as follows: t x = , 2 t y = , 3 t z = , 1 ≤ ≤ t . (b) r F d C ⋅ ∫ where F ( x, y, z ) = xy i + yz j + zx k and C is the same curve with the same parameterization as the one in part (a); i.e. t x = , 2 t y = , 3 t z = , 1 ≤ ≤ t . Page 4 of 4 (c) r F d C ⋅ ∫ where > =< xz y z 2 ), cos( , 2 F and C is any path in R 3 from the point (1,0,1) to the point ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 1 , 2 , 1 π . (Use the Fundamental Theorem for Line Integrals.) (d) r F d C ⋅ ∫ where > − + =< 2 2 , xy e y x e y x F and C is the curve that runs along the upper half of the unit circle from (1,0) to (1,0) followed by the line segment from (1,0) back to (1,0). (Use Green’s Theorem.) (e) dx z xy C ∫ + ) 7 ( where C is the line segment in R 3 from the point (1, 2, 3) to the point (4, 3, 2)....
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 Spring '08
 Paris
 Calculus, Line segment, Multiple integral

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