What Are the Practical Uses of Arc Length in Integration?

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Discussion Overview

The discussion revolves around the practical uses of arc length in integration, exploring its applications in various fields, particularly in engineering and physical sciences. Participants express curiosity about the relevance of arc length beyond theoretical understanding and seek concrete examples of its utility.

Discussion Character

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

Main Points Raised

  • Some participants question the practical applications of arc length, seeking specific examples of its usefulness.
  • Others argue that understanding arc length is part of appreciating mathematical structures, regardless of immediate utility.
  • A participant provides an example of calculating the length of cables for a suspension bridge, emphasizing the importance of accuracy in engineering.
  • There is a discussion about whether arc length is specialized knowledge, with some suggesting it may not be necessary for all students, particularly those not pursuing technical fields.
  • Participants mention various scenarios where arc length is applicable, such as movement along curved paths, including the surface of spheres and ellipsoids.
  • Concerns are raised about the relevance of calculus for non-technical majors, with some expressing frustration about needing to learn complex concepts that may not directly benefit their future careers.
  • A later reply highlights that line integrals, which require knowledge of arc length, have applications in electrical engineering.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement regarding the necessity and relevance of arc length in their studies. While some acknowledge its importance in engineering and physical sciences, others feel it may not be essential for all students, leading to an unresolved debate about its broader applicability.

Contextual Notes

Some participants express uncertainty about the necessity of learning arc length in calculus courses, particularly for those not entering technical fields. There is also a discussion about the varying levels of interest and difficulty associated with calculus, which may influence its perceived usefulness.

madah12
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I always read in applications of integration is to figure out the arc length but they never tell us what is it good for I also couldn't find immediate results by using google, so can anyone tell me its uses?
 
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Well, when do you figure it might be useful to find a length of some curve?

Personally, I find it interesting that you can find that property, rather than "useful".

If you can't develop an interest for studying mathematical structures as such, you should seriously consider quitting maths.
 
I am not a math major so I can't quit it I am just asking what are its applications I am not saying I want to use them.
 
Arc length is only one of many possible applications of the integral. Some other include the area beneath the graph of a function, the volume of a solid, the work done in moving an object along some path, the distance an object travels, given its velocity, and many, many more.
 
no I meant what are the uses of the arc length
 
You do understand that it is useful to measure things, don't you? That's why every hardware store, drug store, or five and dime sells rulers! Rulers are good for measuring straight lines, but not everything you need to measure is a straight line.

We could give examples showing how using "arclength" as a parameter simplifies some problems but whether or not that would seem "useful" to you depends upon what you mean by "useful"- and we have no way of knowing what that is.
 
well ok does there exist any problem that we need to use the arc length to solve or simplify? second does the arc length of a function have any application in science like physics or chemistry?
 
OK, I'll give you a specific example. You are an engineer charged with building a suspension bridge. The cables are one of the most expensive parts of the bridge and you need to order them from the steel manufacturer. How long do they need to be? You need to give the manufacturer an accurate figure. If you get it wrong, you will probably get fired, and your career will be ruined. Using calculus, you can accurately calculate the length of the cables.
 
phyzguy said:
OK, I'll give you a specific example. You are an engineer charged with building a suspension bridge. The cables are one of the most expensive parts of the bridge and you need to order them from the steel manufacturer. How long do they need to be? You need to give the manufacturer an accurate figure. If you get it wrong, you will probably get fired, and your career will be ruined. Using calculus, you can accurately calculate the length of the cables.

ok but then I think that it is more specialized knowledge ,so people who take calculus II don't need to learn it shouldn't they keep it for only math majors or civil engineering majors. I am saying that because I feel it is a pity that not being good in something understanding something won't be very useful to me affects my future.
 
  • #10
When you say "math and civil engineering", do you think the example I gave is the only example where calculus is useful? Trust me, any form of engineering or physical science will use calculus in some form or other. But it is in fact a type of specialized knowledge that won't be of much use if you are a salesman, for example. You can also look on calculus as something that an educated person should know, which is what I was told when I voiced similar complaints about the many hours I wasted studying literature when I was in school.
 
  • #11
Whenever something moves from one location to another along any path other than a straight line, the distance traveled is the arc length. (Actually, even travel along a straight line is an application of arc length, but you don't need calculus for that.) Examples:

Movement along the surface of a sphere (e.g. the surface of the earth);

Movement along the surface of an ellipsoid (e.g. a more accurate model of the surface of the earth);

Space flight-- spacecraft don't move in straight lines.

I suppose you know the formula for the circumference of a circle; that's an application of arc length.
 
  • #12
madah12 said:
ok but then I think that it is more specialized knowledge ,so people who take calculus II don't need to learn it shouldn't they keep it for only math majors or civil engineering majors. I am saying that because I feel it is a pity that not being good in something understanding something won't be very useful to me affects my future.

What would you consider unspecialized knowledge? Writers don't need calculus at all, why teach it to everyone to begin with?!

Honestly it sounds like you're just finding an excuse for not liking it or not being very good at it.
 
  • #13
Feldoh said:
What would you consider unspecialized knowledge? Writers don't need calculus at all, why teach it to everyone to begin with?!

Honestly it sounds like you're just finding an excuse for not liking it or not being very good at it.

I am not saying it as an excuse "I am saying that because I feel it is a pity that not being good in something understanding something won't be very useful to me affects my future." I am saying I am not good at it, but I am saying it is a pity that I have to be good in it to have a good future.
 
  • #14
In what way does it affect your future? Are you planning to go into a technical field? If not, then having trouble with calculus will probably not impact your future greatly - you are certainly not alone! If you are planning on going into a technical field, then it is important to learn calculus. What are your plans?
 
  • #15
well I am a freshman in an electrical engineering program but I don't necessarily like engineering I am just looking for something that is interesting and that pays well, so I could change my major maybe finance but it still involves calculus which I am fine with as long it is easy calculus, and basically I feel overwhelmed by things from calculus that I see as difficult and hard to find interest in. At least in first year physics I enjoy what I study because it feels more real to me and the only thing I needed from calculus is basic integration and basic differentiation and it is my opinion that that's all they should teach for freshmen.
 
  • #16
My advice is that if you find calculus difficult and/or uninteresting, you should re-evaluate whether engineering is the right career for you.
 
  • #17
To calculate a Line Integral, you have to know how to compute an arc length. Line Integrals has many applications in Electrical Engineering...
 

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