Question

(1 point) Let F = -5yi + 2xj. Use the tangential vector form of Green's Theorem to compute the circulation integral SF. dr where C is the positively oriented circle x2 + y2 = 1.

Answer 1

DO$3121 riven that F = -547 -+ 2x] Now, (F. di Fodr = (542 +245) (bl 2 + dys) al Į P. de J - 54 dn + sedy C Here, DM M = -54 ) =-5 and N 2x ON ӘХ 2 an By crreen's Theorem LON Į P. do - M dyda Pid? = {()-(-5)) dy dse & Fods 27 f dy de since, I dyda denotes here 2124-4²=P a where, ( 1 ) C area of Circle sadies (o)= d. and Area of Circle - T2 Area of circle Ta12 Area of circle 2 le. dyda -T n] be Comes, we have equation rids [p 7 X X = 7T

solen Given that paat Ody Area can be written as Jordy - Jas-39)ady Jords Lee By Jedy fout for appropriately chosen pand &. let is assume Pro and aan Then, O DL Dg and so on and 2P ду 20 Du do above values = using of P, Q o ap) in D, we have I andy = 1, 1. dedy = fode + oldy - andy fady Jordy I andy Here, I dody of ellipse D ככ denotes the area D and b=16 + y² - ) where, a=14 (16)2 Area of ellispe = tab ellipse = TX14816 Area of ellispse = 224T equation 2 becomes, = 224T x2 (192 and = Arla Әр
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