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Math Help - Arc Length

  1. #1
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    Arc Length

    Having trouble findin the Arc length of this curve.

    x=(1/3)(sqr*(y))(y-3) 4<y<25

    I found the first derivative: (sqr*(y)/2 - 1/2sqr*(y)) Is that right?

    Then put it into the arclength forumule to set up the integral
    sqr*(1+ (sqr*(y)/2 - 1/2sqr*(y))^2)

    Now sure how to simplify the terms underneath.
    Last edited by NickytheNine; April 17th 2009 at 11:51 AM.
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  2. #2
    MHF Contributor
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    Hi

    Is it x = \frac13\:\sqrt{y(y-3)} or y-3)" alt="x = \frac13\:\sqrt{y}\y-3)" /> ?
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  3. #3
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    The second one ha sorry i wasnt clear (1/3)(sqr*(y)) (y-3)
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  4. #4
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    OK y-3)" alt="x = \frac13\:\sqrt{y}\y-3)" />

    Hence I agree with your derivative : \frac{dx}{dy} = \frac{\sqrt{y}}{2} - \frac{1}{2\:\sqrt{y}}

    And

    \sqrt{1+\left(\frac{\sqrt{y}}{2} - \frac{1}{2\:\sqrt{y}}\right)^2} = \frac{\sqrt{y}}{2} + \frac{1}{2\:\sqrt{y}}

    and you're done !
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