Homework Help: Length of a curve

1. Nov 1, 2011

lmh4

1. The problem statement, all variables and given/known data
Find the length of the curve.

x=cos(2t)
y=sin(3t)
0≤t≤2∏

I know the length is just the integral from 0 to 2∏of the magnitude of the velocity.

3. The attempt at a solution

x'=-2sin(2t) x'^2=4sin^2(2t)
y'=3cos(3t) y'^2=9cos^2(3t)

c=∫√4sin^2(2t)+9cos^2(3t)

Im having trouble evaluating the integral. Could some please point me in the right direction?

Thanks

2. Nov 1, 2011

HallsofIvy

$4sin^2(3t)+ 9cos^2(3t)= 4sin^2(3t)+ 4cos^2(3t)+ 5cos^2(3t)= 4+ 5cos^2(3t)$. Let $u= 4+ 5cos^2(3t)$.