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Length of function

by daniel_i_l
Tags: function, length
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daniel_i_l
#1
Nov18-05, 04:35 AM
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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?
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TD
#2
Nov18-05, 04:41 AM
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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
daniel_i_l
#3
Nov18-05, 04:47 AM
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Thanks!

James R
#4
Nov18-05, 06:37 PM
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Length of function

You're talking about arc length, right?
TD
#5
Nov19-05, 12:40 PM
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Yes, at least that's what I assumed.


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