Question

6. [0/7.69 Points] DETAILS PREVIOUS ANSWERS LARCALC11 15.3.506.XP.MI. Find the value of the line integral Ter F. dr (Hint: If F is conservative, the integration may be easier on an alternative path.) / (x² + y2) ox x2 + y2) dx + 2xy dy (a) r(t) = t'i + t?j, Osis 2 84/3 X (b) r2(t) = 3 cos(t)i + 2 sin(t)j, Osts I 2 37.483 х Need Help? Read It Master It Talk to a Tutor Submit Answer

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Answer 1

Solution Given that F: 100 ye days Sredo o line integoal $.60tys datboyay o Z Z Z Foomula :- Fundamental Theorem of line Enepal suppose that is a smooth cutive given y Bla), astsb. thal foo a function whare poadient recloo jf is continuous on 6. Also suppose Then s ģF : D3 - F1866)) - FC860)) G hose 8 = cofya, ? + 2y Then ox 1 L-> Ê Bay OZ 2 2 aty aay 0 olto + cay-2y) since oxZ 8 B is conservative bet F = of. Then

Than OF = 2 Coxips i + 20y 8 f et ta on atz F: Sla*nya)do ces stage – 0 &ti 1+1 Fs and of - 207 ช F: Szay oly FRouge ☆ f=ay 2 foom Equation and @ 2 @ 2 f tay [writing common team) & vf whool f: & tof - Songs dat day dy = {P. do F 22.62) - FC8601). F(8.4) - F10,0) [using Fundamental Thcoocom] [: 0,12)=40*4 + ſe osts2 0, (2) = (237623 04607-0 : 8i+uj] . Brexub-o 5134198 : 513+384 [foon ] I 896 3

(3 896 = 3 6 Similarly oste 8(2): 300Mb) î+ 2 finales 0; 10) = 360360) î + gincajú 0260) zito {:609 (0)=1 din (0)=0 0,(4) - 3600(4) + asin(3) coon: 0 i]. 82 ( 2 ) = 0 +2 sin I Scaryoda laaddy 17.08 FCCT)) - FC8601) · F(0.2) - F13.0) should corca)? - [ 07 +601608" [ using Equalon oraya 0- -9 Angweto @ 896 3 6 -9 X

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