Question

Find the exact length of the curve. 36y2 = (x2 - 4), 5 SXS6, y20 -/20 points SCALCET8 8.1.015. Find the exact length of the curve. y = In(sec(x)), OS XS 8/3

Answer 1

Given 36y² = (224); senso; 920 Tength of coove aga rit (dega ix] 36y² = (x2-4)3 Biff with respect to a 36 S 22" 362ydo 36-4328 (4+) 724 dy = 3 (-4) (22-0) de la Ge Col? - 4² from y = (2-4)/2 72 y 31 on ( _42 3 & 30 - CP-439. (8-4) 2

=> [*] 035 Lda 22 VI+ length of corre = 16 (2-1) 2x Jardn = ah] ni - [69.53] - (6-5) - - - 9685 Erad length of corre = 2 1 Exact length of cossre - [14.1666] Corve Enach corre = /14. 1666

6) Giren y= ln ( sec (x)) , Osnal length of corre - So it (dega de where as b= lower kmito Upper limit - I Seca - y = ln (sec (A)). Diff with respect to 'x' dy - ln (secas) dalna a seconda ded) a seca=seca tann = seca- tanx It tanto = seco du - tanx length of corre = (t it tanda da la secx de = (T3 seca dx loose cattanx = ln (seca + tann) "3 Secade = ln (sec. II + tan I) - ln (secot tano) = ln (2 + 55 ) – en CD = ln (2+3) .o Tength of corre = ln (2+53) (81) ✓ Length of couve - 1.3169 /