Question

2t from Find the length of the parametric curve given by r(t) = 2 – logt and y(t) t=l to t= e.

Answer 1

> An's Given X(t)= +"-logt , y(t) =ąt from t= to tre We know if a= f(t), and y = g(t) then Let<ß dog B Length = de dt + .)+ (dy)2 dt d > x = t - logh di ct-logt) dx a (logt) = 1 da dt = 2t- t d dt tn = ntni y=at dy dt ola Cat) 1 = a d. (t) = 2(1) de [i am (t) =] dy da こ2

e Length = ? Hidt ܢ ri La pool' } dodol de dy debljina Jodoh hotosero) BEORD34 ons boimage) 923b v (at- +3+ (2)² dt [-(4-6)= a +5-226] 2:24 2.2k +4: dt V4737c7) 5-2-ax +4 e S 4t+1-4+* dto t? fram 4+4+1 t2 dt e 4+4+1 rez dt e n 11 4+++1 t dt

put u= 4+1 = 0 การรับ 16+3 dt= I du 1188009 16+3 From 4+4+1=4 = 4+4=u-1 = t4 = 2+1 If t=1 » u = 40% = 1 = 5 » u = 4eft = 1 = 4 * 13/7 m2 - t=e 4 4e4t) dt- V4+4+1 vu t spiļus us us toplano at ist du ť 1673 metro planos 4e + at .du E4 5 4e4u va 416 S ordt town ... duhet (201712 s radusi to arquite 4e4+1 4 U-1 put v=vu -> Veu dive du 21a 1 die = tida 2 va dv Ida > du=evdio 2V 2 13359333 u=4e*+1 U=v4e +i U-5 و دوا د If If

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La Va etti २ vs 2 E ++ (lautetu +.) - toldtetti - 1) – en (15 +1) +en(6-1) ) L = 6.4947 Length = 6.4947