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2. Use Greens theorem in order to compute the line integral $ (x - 1)3 dy - (y-2): d.x where C is the circle of radius 3 cen

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Given line integral & (2-4)3dy -(y-2)3 dx ROS Where c is the cinde of radius3 centered at (2,2) and traversed in the counterLet R be aregion bounded by c, the circle of radius 3 centered at (112) le. R: (x-2)² + (-2)² = 32 NOW, & (x-4)3 dy -(y-2)3 dང E->( - ༤) ར - ( - 1 Pay ༤ - [ $ (- ༢༠) - > (དg-༠༩)] 4,4y Greens theorem = - })[ - 3(ཀ-ད– - 3 (སྶ-༧) ] a dySS (01-17²+ (9-272) dx dy ose the parametric equations tor R, 2-1 = rocoso, 4-2= yo sino ,OST<3,030 <2TC jen z = 1 + pocoso,J = 0(217) Orriol lön do 24 ои coso arsinol sino rcoso 2 2 E rcosto + go singo = m (cose +simo) = m Fi sino +20s0-] 2The above integral becomes 2TC 3 of [ frcoso)2+(rsine 2 ].adrdo COSO 0=o rzo 2 Te 2 p2 cos²o ap2 sin² otapdrdo 0=o p=0 • Te rا ] ) ([2]) :: ( ::().( همد) : اپنی ۵ ۴ 3 مني و به اجرای ۲۰ 6 = بل -2 =| - 3. ([2 ]). ([ - 1) - 3. (20-9)([ 쑥 - ] ) - 3.2. = 3.TC. |»(ཀ- ay - (༡-༠༧ ༡ ༢ བུཉྩ༌ 2 2T 2

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