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Length of function 
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#1
Nov1805, 04:35 AM

PF Gold
P: 867

My friend told me that they had just learned an equation to find the length of a function. I decided that it would be cool to try to find it myself. I got: [tex]
L(x) = \int \sqrt(f'(x)^2 +1)dx [/tex] I got that by saying that the length of a line with a slope of a over a distance of h is: [tex] \sqrt(f'(x)^2 +1) [/tex] Am I right? 


#2
Nov1805, 04:41 AM

HW Helper
P: 1,024

In general, when a function f is determined by a vectorfunction (so you have a parameter equation of the curve), the arc length is given by:
[tex]\ell = \int_a^b {\left\ {\frac{{d\vec f}} {{dt}}} \right\dt}[/tex] There are of course conditions such as df/dt has to exist, be continous, the arc has to be continous. Now when a function is given in the form "y = f(x)" you can choose x as parameter and the formula simplifies to: [tex]\ell = \int_a^b {\sqrt {1 + y'^2 } dx} [/tex] Which is probably what you meant 


#4
Nov1805, 06:37 PM

Sci Advisor
HW Helper
PF Gold
P: 562

Length of function
You're talking about arc length, right?



#5
Nov1905, 12:40 PM

HW Helper
P: 1,024

Yes, at least that's what I assumed.



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