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Math Help - length of the given curve

  1. #1
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    length of the given curve

    one of my HW problems is to find the arc length of the given curve for x=t^2, y=(3^{1/2}4/3)t^{3/2}, z=3t, 1 <= t <= 4

    now i have the definite integral that goes from 1 to 4, with the equation (4t^2 + 12t + 9) dt.

    but how do I solve this integral? it seems too hard
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  2. #2
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    Quote Originally Posted by Arez View Post
    one of my HW problems is to find the arc length of the given curve for x=t^2, y=(3^{1/2}4/3)t^{3/2}, z=3t, 1 <= t <= 4

    now i have the definite integral that goes from 1 to 4, with the equation (4t^2 + 12t + 9) dt.

    but how do I solve this integral? it seems too hard
    <br />
l=\int_1^4 \sqrt{\left(\frac{\partial x}{\partial t}\right)^2+\left(\frac{\partial y}{\partial t}\right)^2+\left(\frac{\partial z}{\partial t}\right)^2} \ dt \ = \ \int_1^4 \sqrt{4t^2+12t+9} \ dt \ = \ \int_1^4 (2t+3) \ dt<br />
    Last edited by mr fantastic; September 18th 2009 at 08:38 AM. Reason: Restored original reply
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