Multivariable Calculus Unit 8: Arc length and Curvature

We derive the arc length formula (illustrating how we can use difference quotients and Riemann sum). Then we compute arc length in a few examples, in 2, 3 and even 4 dimensions, then define curvature and TNB frame.

P.S. Some thing just noticed after uploading: in the computation of the arc length of the parabola, we have not arcsin but arcsinh. arcsinh is the inverse of the function sinh(x) =(exp(x)- exp(-x))/2.

[austinwilliams]

@ 20:45, that's arcsinh(t), not arcsin(t), no?