Parameterization

Section 3 Arc Length

Definition Let x = f(t), y = g(t) and that both dx/dt and dy/dt exist on [t 1,t 2 ] The arc length of the curve having the above parametric equations on the interval [t 1,t 2 ] is defined to be:

Example

Find tha arc length L of the curve: x=rcost, y=rsint ; 0 ≤ t ≤ 2 π, where r is a constant ( what does that represent?) Solution:

Homework 1. Find tha arc length L of the curve: x=2cos3t, y=2sin3t ; 0 ≤ t ≤ π/3, ( what does that represent?) 2. Find tha arc length L of the curve: x=4cos3t, y=3sin3t ; 0 ≤ t ≤ 2π/3, ( what does that represent?)