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February 16th, 2011, 10:07 PM  #1 
Member Joined: Jan 2011 Posts: 30 Thanks: 0  The length of a curve with logaritm (Natural)
Hi guys the problem is to get the length of the curve y= ln(x^21) 0<= x <= 1/2 As far as I am concerned we can use a formula L = $(from a to b) SQRT [1+ f'(x)] dx I don't know how to get the derivative of the function, could someone help me complete this task 
February 16th, 2011, 10:37 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: The length of a curve with logaritm (Natural)
In your formula, you need to square f'(x) in the radicand of the integrand. While the integral will return a real value, is it meaningful? The curve is not defined on [1,1], although WA shows it has a real and imaginary part on this interval. It looks like the same result would be returned by using which is defined on (1,1). Also confusing to me is that WA shows the same graph for both functions. 

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curve, length, logaritm, natural 
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