Asked by Marie

Let c be a curve w/parameterization r(t). show that the line integral of T dr equals the length of the curve where T is the unit tangent.
Answered by collins
am not even conversant with those .....i don,t know
Answered by Steve
Hmmm. Let me dig out my text on differential geometry. Meantime, try googling the topic in vector analysis.
Answered by Steve
Actually, just consider the definition of T.

Take a peek here, and it should be clear, since the arc length is just

∫ ds = ∫ |dr/dt| dt
Answered by Steve
oops: here is

http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/arc/arc.html#alfunction
Answered by collins
hmmm i got to write these down wow