Vector Calculus - parametrize the arc length

A short video to Vector Functions explaining writing in terms of the arc length.

Check out www.gaussianmath.com for more content on vector calculus.

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• vector
• calculus
• donny
• gaussian
• math

[lymsfriend]

awesome teaching..but the view of the white board quite not clear and ur written...tnx for the upload..donnylee..

[donylee]

Sorry about that. This was during my earlier videos where I was trying to get the calibration of the camera correct.

[almeidabatista]

2. In general, the parameter and the arc length are not linearly related (although they are in this particular case). Actually, depending on the particular curve you are parametrizing, the arc length integral might be even not possible to determine analytically.

I don't understand step 3 though. I think the outline is finding the arc length in terms of t then finding t in terms of the arc length then substituting back.

[simplystimpy]

is there a video that comes before this one? I can't find it.

[LongShlong125]

1. find length by int(||f(x)||, o , t);

2. You Should get something like S=a*T where a is a constant of some sorts (in this narrow case) rewrite in terms of t=S/a and substitute back in the equation.

3. Differentiate the equation for S , rearrange to isolate ||f'(s)|| and get one.

4. profit?

I will start having my notes as comments(and start having them) from now on, just to try and contribute.