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Math Help - can't solve this arc length integral

  1. #1
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    can't solve this arc length integral

    find the length of the curve of r(t)=<2t, t^2, (t^3)/3>

    so i take the derivative of each, and then square them and get

    <4, 4t^2, t^4>

    and the formula is srqt (4+4t^2+t^4)

    and i need to find it from t=1 to t-2.

    i just don't know how to solve that integral. it doesn't really seem possible. can anyone help with that? thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by isuckatcalc View Post
    find the length of the curve of r(t)=<2t, t^2, (t^3)/3>

    so i take the derivative of each, and then square them and get

    <4, 4t^2, t^4>

    and the formula is srqt (4+4t^2+t^4)

    and i need to find it from t=1 to t-2.

    i just don't know how to solve that integral. it doesn't really seem possible. can anyone help with that? thanks
    Hint: t^4+4t^2+4 = (t^2+2)^2.

    Now can you proceed?
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  3. #3
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    ah, always a simple solution. thanks for pointing that out!
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