Calculus 2: Finding Arc Length | Florida A&M Univ.

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    Arc Arc length Length
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Discussion Overview

The discussion revolves around the challenges of finding arc length in calculus, particularly focusing on the integral formula for arc length and the algebraic complexities involved. Participants share their experiences and seek insights into simplifying the process, while also touching on related mathematical concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • The original poster (OP) expresses frustration with the tedious algebra involved in calculating arc length and inquires about potential shortcuts.
  • One participant suggests that the algebra should not be a major concern and mentions that the integral for arc length is rarely expressible in elementary functions, using the ellipse as an example.
  • Another participant points out a potential error in the OP's derivative notation and notes that functions are often structured to simplify the algebra, recalling experiences with sine functions.
  • There is a discussion about the term "rigged," with participants explaining that it refers to setting up functions in a way that makes calculations easier.
  • One participant admits to not knowing what an ellipse is, prompting further clarification and humor about basic geometric knowledge.
  • Further discussion includes a reference to "rigged Hilbert space," with one participant acknowledging their lack of knowledge in that area while providing a link for more information.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the ease of finding arc length, as opinions vary regarding the complexity of the algebra involved and the understanding of related concepts like ellipses and rigged functions. The discussion remains unresolved on several points, particularly regarding the foundational knowledge expected in calculus courses.

Contextual Notes

There are indications of missing foundational knowledge among participants, particularly concerning basic geometric shapes and the implications of certain mathematical terms. The discussion also reflects varying levels of familiarity with calculus concepts, which may affect the understanding of arc length calculations.

Techman07
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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.
 
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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:
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.
 
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.
 
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?
 
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 :-p

Daniel.
 
Examples...

I guess that i should give an example, but what is an ellipse?
 
You have to be kidding,right...?Tell me you are.


Daniel.
 
Nope, not kidding, never used the term in calculus I, haven't seen it yet in cal II
 
  • #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, wouldn't I? :P
 
  • #11
Nope, not kidding, never used the term in calculus I, haven't seen it yet in cal II

lol, that's because you first encountered the term in pre-school or 1st grade (whenever you begin learning about basic shapes.)
 
  • #12
well, thanks for input.
 
  • #13
whozum said:
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, wouldn't I? :P

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

Daniel.
 
  • #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 don't 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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