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Anss P(x,y) = Y+9 х?у? (x, y) +lo,0) 1x, y) [6,0) Со (x,9) -X +9 х+у 2 (x, y) + (0,0) ( x, y) [o, o/ | Р, О) Fis gradient vector field of да ду - ӘР Әу Ә0 6. - 34 [-] (Y'ky2)( - ) -1-X +y) - 25 (х+у2 )2 - - y'+2° 2х9 (х+угу 2 (р ү? у 2xy gin (Y*+ y? ) 2 х'y? ))) - +ү ну) 2 3 (х+у2 )2 хуу? 9xy - 2y 2 1x? +y? ) 2 уу?- 2xy (х+у2 ) 2. 2х So 20 ӘР 29 F is gradiet vector field Э
2 (6) D = {x 2099 +y 2020 - 13 s Pdx tady = 0 • for closed boundary F is gradient So I a fun g such vector field thot F=7g So integration with respect to closed boundary will be zerool for same initial and ending point on boundary) 'I = S pdx + ledy (C ) ƏD By using green tim I = Ss 126 ӘР ay schody ƏX = Sslap ӘР ӘР dy - Jy IP ly) dedly By Las part D No calculation is part (b) donot violate green's thm.
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