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Math Help - arc length and parameterized curve length

  1. #1
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    arc length and parameterized curve length

    help would be much appreciated becasue i have been trying and cannot find out how to do these two problems.

    1) Find the length of parametrized curve given by
    x(t) = 0t^3-3^2+6t, y(t)= -1t^3+3t^2+0t t from 0 => 1

    and i know L = integral (0 to 1) sqrt( (-6t+6)^2 + (-3t^2+6t) )

    but do not know how to proceed through the integral and all..

    and 2) Find the length of the arc formed by
    x^2 = 10y^3
    from point A to point B where, A = (0,0) and B = (100,10)

    no idea where to go on that one and help ASAP would be great seeing as its due soon.

    thank you once again for any help
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  2. #2
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    Quote Originally Posted by covette View Post
    help would be much appreciated becasue i have been trying and cannot find out how to do these two problems.

    1) Find the length of parametrized curve given by
    x(t) = 0t^3-3^2+6t, y(t)= -1t^3+3t^2+0t t from 0 => 1

    Mr F says: I can't understand the expressions you've posted for x(t) and y(t). Please clarify.

    and i know L = integral (0 to 1) sqrt( (-6t+6)^2 + (-3t^2+6t) )

    but do not know how to proceed through the integral and all..

    and 2) Find the length of the arc formed by
    x^2 = 10y^3
    from point A to point B where, A = (0,0) and B = (100,10)

    no idea where to go on that one and help ASAP would be great seeing as its due soon.

    thank you once again for any help
    2) Start by differentiating y = \left( \frac{x^2}{10}\right)^{1/3} and substitute into the usual formula.
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