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The arc length .

  1. May 22, 2005 #1
    The arc length.....

    Hello all, this is my first post. I am a Computer Engineering Student at Florida A&M University taking Calculus 2 over the summer semester.

    Should finding the arc length be so extensive?? Are their shortcuts that I am missing?

    If you don't know the formula, the arc length is the integral from a to b of


    [1 + (f'(x))^2]^1/2

    If finding the arc length IS this difficult, can someone direct me towards some insight. I get caught up in the VERY tedious algebra involved.

    thank you.
     
  2. jcsd
  3. May 22, 2005 #2

    dextercioby

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    Well,the algebra should be a snack.I mean,it should be the least worrying.

    The integral [tex]\int_{a}^{b} \sqrt{1+\left[f'(x)\right]^{2}} \ dx [/tex] is on rare occasions expressible in terms of elementary functions.

    Think the ellipse.Try to compute the length of the ellipse...:wink: You'll see that algebra won't be a problem at all.

    Daniel.

    P.S.Surely,that formula is valid in cartesian coordinates.You can Switch to polar,if u find the integration to be easier.
     
    Last edited: May 22, 2005
  4. May 22, 2005 #3
    You have the wrong sign on your f(x) derivative dex.
    OP: You'll mostly find the functions rigged so that the algebra is really simple. I remember mostly arclength of sin functions in my class.
     
  5. May 22, 2005 #4

    dextercioby

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    Thanks for pointing it out.What does this " You'll mostly find the functions rigged "mean...?(Sorry,it's a bit offtopic,i guess,but i have no idea what that means).

    Daniel.
     
  6. May 22, 2005 #5
    Rigging something means setting it up so that something specific happens. For example, for the arclength of the cos function you get [itex] \sqrt{1-sin^2x} [/itex] which is just cos(x).

    Are you belgian native?
     
  7. May 22, 2005 #6

    dextercioby

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    Nope,i'm Romanian and for about a week i'm wondering how should i translate "rigged Hilbert space" into Romanian.This word "rigged" has been obssessing me :tongue2:

    Daniel.
     
  8. May 22, 2005 #7
    Examples....

    I guess that i should give an example, but what is an ellipse???
     
  9. May 22, 2005 #8

    dextercioby

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    You have to be kidding,right...?Tell me you are.


    Daniel.
     
  10. May 22, 2005 #9
    Nope, not kidding, never used the term in calculus I, haven't seen it yet in cal II
     
  11. May 22, 2005 #10
    You should know what an ellipse is from geometry.

    Dex, I'd help you out, but first I'd have to know what a Hilbert space is, wouldnt I? :P
     
  12. May 22, 2005 #11

    Gza

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    lol, that's because you first encountered the term in pre-school or 1st grade (whenever you begin learning about basic shapes.)
     
  13. May 23, 2005 #12
    well, thanks for input.
     
  14. May 23, 2005 #13

    dextercioby

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    It's a complete preHilbert space.What does "rigged" mean...?

    Daniel.
     
  15. May 23, 2005 #14
    Rigged

    Rigging something means setting it up so that something specific happens. For example, the rigged equation above is set up so that once you solve the correct problem, the result is really simple to evaluate. It simplifies easily due to the properties of the function. If it wasnt rigged, fro example if f(x) = 3x^3, then the integrand is considerably more difficult than if it was just f(x) = cos(x).


    Rigged hilbert Space

    I dont know anything about hilbert spaces, I haven't began quantum mechanics yet, but I'm sure this will help you out:

    http://en.wikipedia.org/wiki/Rigged_Hilbert_space
     
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