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Math Help - Finding path length of curve

  1. #1
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    Finding path length of curve

    Find the path length of y= (x^3)/(a^2) + (a^2)/(12x)

    I know I'm supposed to be integrating ds = dx (1+ (dy/dx)^2)^1/2

    but i'm having trouble simplifying the expression inside the square root..

    thanks in advance!
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  2. #2
    Super Member
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    so the derivative is   \frac{3x^2}{a^2}  - \frac{a^2}{12x^2}

     1 + (y')^2 = 1 + \left(\frac{3x^2}{a^2}\right)^2 - \frac{ 6 }{12}+ \left(\frac{a^2}{12x^2}\right)^2  =  \left(\frac{3x^2}{a^2}\right)^2 + \frac{ 1 }{2}+ \left(\frac{a^2}{12x^2}\right)^2 = \left[\frac{3x^2}{a^2}  + \frac{a^2}{12x^2}\right]^2

    that means you should then evaluate the integral

     \int  \frac{3x^2}{a^2}  + \frac{a^2}{12x^2} ~dx
    Last edited by mr fantastic; October 21st 2009 at 05:56 AM. Reason: Made brackets large
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