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Math Help - length of a curve

  1. #1
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    length of a curve

    Hi, i am trying to find the arc length of a curve over y=x^(2/3) from x=1 to x=8. I know that in order to use the length equation i have to find 1+[f '(x)]^2 which equals 1+(4/9)x^(-2/3). The next step in my book turns that into (9x^(2/3)+4)/(9x(2/3)). I cant figure out why they did that, can anyone help me.
    thanks
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  2. #2
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    Quote Originally Posted by cowboys111 View Post
    Hi, i am trying to find the arc length of a curve over y=x^(2/3) from x=1 to x=8. I know that in order to use the length equation i have to find 1+[f '(x)]^2 which equals 1+(4/9)x^(-2/3). The next step in my book turns that into (9x^(2/3)+4)/(9x(2/3)). I cant figure out why they did that, can anyone help me.
    thanks
    1 + \frac{4}{9} x^{-2/3}


    = 1 + \frac{4}{9} \frac{1}{x^{2/3}}


    since x^{-2/3} = \frac{1}{x^{2/3}}. Get a common denominator:


    = \frac{9 x^{2/3}}{9 x^{2/3}} + \frac{4}{9 x^{2/3}}


    which turns into what the book has once you add the two fractions together.
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