Question

(a) Let X(s) = (x(s), y(s)) be a plane curve parametrized by arclength. Show that the curvature is given by the formula
κ = |x'y'' − x'' y'|.

b)Show that x(s)= ((1/2)(1-s^2),(1/2)(cos^(-1)(s) - s(sqrt (1-s^2)) is parametrized by arclength, and compute its curvature.

Really need someone help me about this question.
I have thought almost 1 day.

Answer 1

is 's' arclength?

Answer 2

\[ s - \int \sqrt{1 + (dy/dx)^2} dx \] ??

Answer 3

=

Answer 4

Yes s is arclength

Answer 5

is that the complete formula

Answer 6

http://en.wikipedia.org/wiki/Radius_of_curvature_(mathematics)