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Math Help - length of curve

  1. #1
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    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!

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  2. #2
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    Quote Originally Posted by alex_nicole View Post
    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 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 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 \sqrt{2}

    and we do it 8 times so we get

    8\sqrt{2}

    Yeah.

    Or you could do it with an integral, but why? It is too much work.
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  3. #3
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    Thanks a bunch, but just out of curiosity, how would you start it with integrals??? Just in case the calc teacher asks...
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