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October 23rd, 2016, 12:39 PM   #1
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Calculating the line integral of a curve given line segments

I have the curve and I wish to integrate the curve: (x^2 dx + y^2 dy + z^2 dz).

Notation wise: A "C" as in to displace the bottom limit of an integral (I will attach an image so that it is easier to visualise).

Image: Maths - Album on Imgur

And the aforementioned curve consists of the line segments from (zero,one,zero) to (one,zero,one) and then from (one,zero,one) to (two,one,three).

I anticipate that there will be a kink/sharp twist in said curve.

With the boldened information being the most relevant - how would I solve this integral?

So far, I have got this:

x=xA+t(xB−xA) dx=(xB-xA)dt.

y=yA+t(yB−yA) dy=(yB-yA)dt z=zA+t(zB−zA) dz=(zB-zA)dt.

so

(ds)2=(dx)2+(dy)2+(dz)2(ds)2=(dx)2+(dy)2+(dz)2
ds=||AB→||dt
ds=||AB→||dt
[Although I express doubt and skepticism whether this is right.]

Thank you for any help/assistance given.

Note: The image probably surmises the gist of my question a lot better.

-Nomad609

Last edited by skipjack; October 24th, 2016 at 08:25 AM.
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