# Length of a curve

## Homework Statement

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.

## 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

## Answers and Replies

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HallsofIvy
Science Advisor
Homework Helper
$4sin^2(3t)+ 9cos^2(3t)= 4sin^2(3t)+ 4cos^2(3t)+ 5cos^2(3t)= 4+ 5cos^2(3t)$. Let $u= 4+ 5cos^2(3t)$.