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.

Answer 1

am not even conversant with those .....i don,t know

Answer 2

Hmmm. Let me dig out my text on differential geometry. Meantime, try googling the topic in vector analysis.

Answer 3

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

Answer 4

oops: here is

http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/arc/arc.html#alfunction

Answer 5

hmmm i got to write these down wow