Question

How do you find the length of a curve defined parametrically?

Answer 1

If the curve is defined by a parametric equations `{(x=x(t)),(y=y(t)):}`, then the arc length `L` of the curve from `t=a` to `b` can be found by

`L=int_a^b sqrt{({dx}/{dt})^2+({dy}/{dt})^2}dt`.