Question

eparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s. r(t) = cos 7ti +2j+et sin 7tk (t(s)) = (2+1)0001( a + 1)) +25+(vs + 1}sin(in( tz +1]] x

Answer 1

Q- 94 = et cos i tÝ 574 t e Sined 2 ett cast x' ett (-Sim767.7 + 'cos 71. 27.7 7e?t ( cosit - sin?) 1) 9 2 2 y o ert sinte 7t Costoy & Sinrt.e 7 ?'- ett relt i coste + sind). Now 2 21 =(727+ ( ens 74 -sin 71.)? 141 49 e ( 2 sintt.cast of 49 elldl II- Sin 14 d -1) yle=0 212, 41+ Sin147)

9' (+) - x' ï t ý + 7' : | Я' (51 Sai2+ y' у» 2 z? г (49e"}(t-si»ју)) +о + е!"4 (i+sim 9 1) (49 ч. 2 1e71 р. 1) Are length д х = / 19' (7) 40 77. 7 dt - ул. Ге'' ). - 12 (7) - e“) д Г2 ( 2 ) 7. Я + 1) » e 1, 2 2 - les (+ +1) Г2

So - r(t) = el cos ld i + 2) + ett sinze So prametrized Curve S Replace ell e (2 +) len ( f / 2+1) ht 6/4(3)) = +1) cos [ link en +1)]i+ zj s + 1) sin Ilan las +1)) ir V + Au
You got everything correct except the very first where you wrote 5 instead of s.

Hope this will help