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June 26th, 2008, 10:03 AM   #1
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Arc Length

Does Arc Length under the x axis count as negative arc length?
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June 26th, 2008, 11:23 AM   #2
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Re: Arc Length

[color=#0000FF]Greetings:

If it does, then evaluating the arc length of an arbitrary function, f, would require absolute value where f(x) < 0. However, the process requires the integration of an already positive function. That is, [1 + (f '(x))^2]^0.5 is necessarily positive because the derivative is squared. That said, the answer to your question is, no.

Regards,

Rich B.[/color]
rmath4u2@aol.com
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June 27th, 2008, 09:49 AM   #3
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Re: Arc Length

Thanks for the info, Rich!
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June 28th, 2008, 08:17 PM   #4
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Re: Arc Length

Quote:
Originally Posted by SidT
Does Arc Length under the x axis count as negative arc length?
Another more geometric approach would be to consider that if this was true we would be talking about [color=#FF0000]negative length[/color]. Now does that make sense?
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