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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

You know how calculus can find area under a curve?

Well I was wondering if we could extend this idea

to invent a calculus to finding the length of

the curvy or straight line of a function.

The tangent function isn't exactly right, but it sort of

gives the idea because a function with a large

slope makes a long line between two values of x,

however, if the line is horizontal (like y = 5), then

the length is just difference of two x values, but

the slope is zero, so tangent isn't working here.

(Off the subject, what is tanh (hyperbolic) all about?)

What about pythagoreans theorm, would that help to

find the incremental length at each point based on

√ (dy² + dx²) ???

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Say you want the length of the line on a parabola

fromx = 0 to x=5.

Perhaps , I am not good at calculus yet.

Maybe Length of line =

*Last edited by John E. Franklin (2005-12-11 06:00:08)*

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

This is probably all wrong, but I am learning to use LaTeX!!!

Even if this is wrong, I don't know how to integrate it?

Anyone know where I can learn this one?

...

I found "Power Substitution" on internet.

I might learn this!

...

Well If I let

start, but then gets just as messy as what I

started with, so that's no help...

*Last edited by John E. Franklin (2005-12-11 05:59:33)*

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

I cheated and used a standard mathematical tables integrals answer.

Plugging in 5 and 0, and subtracting revealed a line length of 26.40253635

This might actually be right, since it is a little longer than going

straight from (0,0) to (5,25), and that's because it is a parabola.

Maybe it's right! Hurray! Maybe it's not. I'm not sure yet.

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

What is the length of the curvy line of a sine wave graphed from 0 to 2π radians?

I'll work on this and wish me luck...:)

**igloo** **myrtilles** **fourmis**

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**Flowers4Carlos****Member**- Registered: 2005-08-25
- Posts: 106

you are absolutely correct john! the integral for finding the distance on a curve is how you explained it! although it's a common formula, i find it smart of you (and sooo cute!!!!) that you were able to figure it out on your own!! so smart!!!!

http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/moreApps/arclength.html

as for ∫(1+4x²)^(1/2)dx you either gotta use trigonometric substitution or a table chart (which is also fine). if you want i can solve it "manually" for you... it's not gonna be pretty though.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Thank you very much for the compliment.

You made my day!

I'll check out that link in a minute.

And yes, I did find it in a table, and I got 26.40253635

for the length from 0 to 5 for

I am still struggling with how calculus works, and it is

of great interest to me because I sometimes have to

resort to doing computer approximations by breaking

the problem into the tiny pieces and adding it up.

Newton was a for sure!

**igloo** **myrtilles** **fourmis**

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