(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let c(t) be a path andTthe unit tangent vector. What is [tex] \int_c \mathbf{T} \cdot d\mathbf{s} [/tex]

2. Relevant equations

The unit tangent vector of c(t) is c'(t) over the magnitude of c'(t) :

[tex] \mathbf{T} = \frac{c'(t)}{||c'(t)||} [/tex]

The length of c(t) can be represented by :

[tex] \int_c ||c'(t)|| \; dt [/tex]

3. The attempt at a solution

[tex] \int_c \mathbf{T} \cdot d\mathbf{s} = \int_c \frac{c'(t)}{||c'(t)||} ... [/tex] d-something. dt I suppose.

But this is clearly not quite the arc length integral. So what am I missing? (the book says the answer is the length of c)

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# Homework Help: Integral of unit tangent vector equals arc length?

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