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Math Help - Parametric curves

  1. #1
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    Parametric curves

    I need help finding the length of the curve =/

    x = 5 + 12t^2
    y = 8 + 8t^3

    .. I keep getting the wrong answer when I integrate..

    and the second one is

    x = 7 cos(t) - cos(7t)
    y = 7 sin(t)- sin (7t)

    any help would be great thanks!
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  2. #2
    o_O
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    You didn't give any restrictions on the parameter so I'll just let's just say 0 \leq a \leq t \leq b

    L = \int_{a}^{b} \sqrt{\left(\frac{dx}{dt}\right)^{2} + \left(\frac{dy}{dt}\right)^{2}} dt
    L = \int_{a}^{b} \sqrt{\left[\left(5 + 12t^{2}\right)'\right]^{2} + \left[\left(8+8t^{3}\right)'\right]^{2}}dt
    L = \int_{a}^{b} \sqrt{(24t)^{2} + \left(24t^{2}\right)^{2}}dt
    L = \int_{a}^{b} \sqrt{576t^{2} + 576t^{4}}dt
    L = \int_{a}^{b} \sqrt{576t^{2}\left(1+t^{2}\right)}dt =  \int_{a}^{b} \sqrt{576t^{2}}\sqrt{1+t^{2}}dt
    L = 24 \int_{a}^{b} t\sqrt{1+t^{2}}dt

    etc.

    What are you having troubles with exactly? Show us what you've done for the two integrals and we'll point you in the right direction.
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