My Math Forum finding length of the curve....

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 March 22nd, 2008, 10:24 AM #1 Newbie   Joined: Feb 2008 Posts: 16 Thanks: 0 finding length of the curve.... find the length of the curve ; y=ln(cosx), 0<=x<=pi/3 .
 September 1st, 2008, 08:35 AM #2 Member   Joined: Dec 2006 Posts: 65 Thanks: 0 Re: finding length of the curve.... L(length) = int((1+y’^2) ^0.5)dx (0 to pi/3) = int(1/cosx)dx (0 to pi/3) = int(cosx/(1-sin^2x)dx (0 to pi/3) = int(1/(1-u^2))du (0 to 3^0.5/2) 1/(1-u^2) = 0.5/(1-u) + 0.5/(1+u) L = -0.5(ln(1-u)) (0 to 3^0.5/2) + 0.5(ln(1+u)) (0 to 3^0.5/2) L = 0.5 ln(2+3^0.5)

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### length of curve

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