Question

Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (9y2 - x?)i + (x2 +9y2); and curve C the triangle bounded by y = 0, x= 3, and y = x. The flux is (Simplify your answer.) The circulation is (Simplify your answer.)

Answer 1

F(9y?x?)i + (x2+9y?) ; C: yao, *=3, y: 2 Here 12=3 osne 3 olyea of yoo Flux Pf F= Mi +Ni thens SS (2 + 2 ) dx dy Cirullation, curl= SS come am อฯ dady -② R Given f = (ay²-x²)i + و ЭМ ax am 0-27 .-20 +(x2+9y²) j M = 9y?-x?, N= x++9y? becau) coca?) 2 (94)-2(x) = 9(24) -0 = 187 ду ду ay ON - (z?+94) a (x) + 2y+) = 2X+0 = 22 by siya? Aly) - 4294969 vef) = 0+9(24) = ley ƏN

from o Flur: R 3 x SS(-2x+184) dedy } $ 1-2x+184) dy da o 0 x 3 0 O SES -2x dy +9184 dy] da ${[-2247% + [3] Body *}{-22(x)=(-2260) + 9x?_960*}dx $$-22°+97"}dx=5 az’da - Top 10). 63 3 O .: Flux =163 from ©, circulation Essen on y dx dy Rlou 33 x -SS (20-184) dy da {{ $22dy - Sigydy}dx $[22'47?- (1 421 } dx $22(9)- 22:0) - [978-960']} de }(227-92?)dx = { -12’dr=-621 :-313-09]. 0 3 3 -63 2 circulation -63