Question

in Section 9.3 Problem 4. Find the arc length of each curve; compute one exactly and approximate the other numerically.

a) x=tcost, y=tsint

b) x=t²cost, y=t²sint

for t between -1 and 1

1

Answer 1

Art length of a parameic urve from 七= a to reres d2 J=E Sint X=t lost ノ Given curve 1 (oSt-£ Sint =A dy and (puS int) = Sint + t lost int d+ art erth The (ust tsint)siotte)2 - ap Ju5 2, -

2-1 In (+ 1) 2+ Ln (exact value vaine)) 2 29 5 5 715 (numerical value (bGiven Curve y sint (ost) ost ( -sint +2t los t dt dy +Sint s ct c t 11 7uls 7

A length (-tSint t test) +2t -+ (t st 2t sint)2 t(sint tast+4t(sin^t t 4t

inctio) t4 t'& an even P h V Let, J 2 22 alt 2 22d2 t dt2d2 Ta ble 2 2 3 2 5 S 2 (55- (exact value) numerical value) aproimate 2.1202266