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-   -   The length of a curve with logaritm (Natural) (http://mymathforum.com/calculus/17548-length-curve-logaritm-natural.html)

 Riazy February 16th, 2011 10:07 PM

The length of a curve with logaritm (Natural)

Hi guys the problem is to get the length of the curve

y= ln(x^2-1) 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 :wink:

 MarkFL February 16th, 2011 10:37 PM

Re: The length of a curve with logaritm (Natural)

In your formula, you need to square f'(x) in the radicand of the integrand.

$\frac{d}{dx}$$\ln\(x^2-1$$\)=\frac{2x}{x^2-1}$

While the integral will return a real value, is it meaningful? The curve is not defined on [-1,1], although W|A shows it has a real and imaginary part on this interval. :?

It looks like the same result would be returned by using $y=\ln$$1-x^2$$$ which is defined on (-1,1).

Also confusing to me is that W|A shows the same graph for both functions.

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