Posted by Sarah on Friday, November 16, 2012 at 2:11am.
Find the length of the curve:
y=ln(1x^2), 0<_x<_1/2

CALCULUS  Steve, Friday, November 16, 2012 at 11:12am
s = ∫[0,1/2] ds
= ∫[0,1/2] √(1+y'^2) dx
= ∫[0,1/2] √(1+(2x/(x^21))^2) dx
= ∫[0,1/2] (x^2+1)/(x^21) dx
now use partial fractions to get
= ∫[0,1/2] 1 + 1/(x1)  1/(x+1) dx
= (x + lnx1  lnx+1) [0,1/2]
= (1/2 + ln(1/2)  ln(3/2))  (0+00)
= 1/2  ln3