Length of function

  1. daniel_i_l

    daniel_i_l 866
    Gold Member

    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. jcsd
  3. TD

    TD 1,021
    Homework Helper

    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 :smile:
     
  4. daniel_i_l

    daniel_i_l 866
    Gold Member

    Thanks!:biggrin: :biggrin:
     
  5. James R

    James R 562
    Science Advisor
    Homework Helper
    Gold Member

    You're talking about arc length, right?
     
  6. TD

    TD 1,021
    Homework Helper

    Yes, at least that's what I assumed.
     
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