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March 22nd, 2008, 10:24 AM   #1
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finding length of the curve....

find the length of the curve ;
y=ln(cosx), 0<=x<=pi/3 .
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September 1st, 2008, 08:35 AM   #2
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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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