Arc+Length+of+a+Parametric+Function

Kristen Nocka and Rachel Hendersen

Steps to finding formula for arc length of a parametric curve: 1. Split [a,b] into n subintervals 2. Draw a picture of the curve and some representative line segment 3. Find length of the line segment 4. Use Mean Value Theorem to simplify (3) 5. Sum value found in step 4 6. Find the limit of the value from step 5.

1. a= t0<t1<ti-1<ti 2. 3. Li=[x(ti)-x(ti-1)2 + y(ti)-y(ti-1)]1/2 4.

ti-ti-1 = ∆t

x'(ti)=(x(ti)-x(ti-1))/(ti-ti-1) y'(ti)=(y(ti)-y(ti-1))/(ti-ti-1)

∆t*x'( ti)^2= (x(ti)-x(ti-1))^2

Li=(x(ti*)^2 (∆t) +(y(ti*)^2( ∆t))^1/2

(∆t*y'( ti* ))^2=(y (ti)-y(ti-1))^2

6. L= Integral from [b,a] of (x'(t)^2 + y'(t)^2)^1/2