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

• Techman07
In summary, the conversation discusses the difficulty of finding arc length and possible shortcuts or techniques to make the process easier. The formula for finding arc length is provided and it is mentioned that it can sometimes be expressed in terms of elementary functions. The conversation also touches on the concept of rigging equations to simplify the process and the importance of knowing basic geometric shapes. The term "rigged Hilbert space" is mentioned, which refers to a specific type of mathematical space.
Techman07
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.

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

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

Think the ellipse.Try to compute the length of the ellipse... 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 $\sqrt{1-sin^2x}$ 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

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

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

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.)

well, thanks for input.

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.

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

## 1. What is Calculus 2 and why is it important?

Calculus 2 is a branch of mathematics that deals with the study of infinite series, integration techniques, and applications of integration. It is important because it is used in various fields such as physics, engineering, economics, and statistics to solve real-world problems and make accurate predictions.

## 2. What is the concept of finding arc length in Calculus 2?

In Calculus 2, finding arc length involves using integration techniques to calculate the length of a curve. This is useful in scenarios where the distance traveled by an object along a curve needs to be determined, such as in physics or engineering problems.

## 3. How do you find the arc length of a curve using Calculus 2?

To find the arc length of a curve using Calculus 2, you first need to calculate the derivative of the curve. Then, you use integration to find the length of the curve by integrating the derivative over the desired interval. This will give you the total distance traveled along the curve.

## 4. What are some real-world applications of finding arc length using Calculus 2?

Finding arc length using Calculus 2 has many real-world applications. For example, it can be used to calculate the distance traveled by a car on a curved road, the length of a wire needed to form a specific shape, or the amount of paint needed to cover a curved surface. It is also used in physics to calculate the work done by a force along a curved path.

## 5. Are there any tips for mastering the concept of finding arc length in Calculus 2?

To master the concept of finding arc length in Calculus 2, it is important to have a strong understanding of integration techniques and how to apply them. It is also helpful to practice solving various problems involving arc length, as well as understanding the real-world applications of this concept. Seeking help from a tutor or attending extra practice sessions can also be beneficial.

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