1. ## length of curve

So here it is, I am in calc and I have no clue of where to start:

Find the distance traveled by a particle with position (x,y) = (cos^2(t) , cos^2 (t) ) as t varies in the time integral [0, 4pi]. Compare this with the length of the path on which the particle traveled.

Thanks if ANYONE can help!

2. Originally Posted by alex_nicole
So here it is, I am in calc and I have no clue of where to start:

Find the distance traveled by a particle with position (x,y) = (cos^2(t) , cos^2 (t) ) as t varies in the time integral [0, 4pi]. Compare this with the length of the path on which the particle traveled.

Thanks if ANYONE can help!

if $\displaystyle x=\cos^{2}(t) \mbox{ and } y=\cos^{2}(t)$

by the path is y=x

so when t=0 we are at the point (1,1) and when $\displaystyle t=\frac{\pi}{2}$ we are at (0,0) we will travel back and forth along this line segment 8 times between 0 and 4pi

the distance between (0,0) and (1,1) is $\displaystyle \sqrt{2}$

and we do it 8 times so we get

$\displaystyle 8\sqrt{2}$

Yeah.

Or you could do it with an integral, but why? It is too much work.

3. Thanks a bunch, but just out of curiosity, how would you start it with integrals??? Just in case the calc teacher asks...