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Math Help - Length of a curve

  1. #1
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    Length of a curve

    g(x)=x^3+(1/12x) for 1<x<3

    I can get as far as integral of sqrt(1+9x^4-(1/12x^4)) before running into substitution problems... what should I set U to be? I tried using x^4 but I keep getting screwed up somewhere.. Thanks in advance!
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  2. #2
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    Quote Originally Posted by strawlion View Post
    g(x)=x^3+(1/12x) for 1<x<3

    I can get as far as integral of sqrt(1+9x^4-(1/12x^4)) before running into substitution problems... what should I set U to be? I tried using x^4 but I keep getting screwed up somewhere.. Thanks in advance!
    \displaystyle g(x) = x^3 + \frac{1}{12x}

    \displaystyle g'(x) = 3x^2 - \frac{1}{12x^2}<br />

    \displaystyle [g'(x)]^2 = 9x^4 - \frac{1}{2} + \frac{1}{144x^4}

    \displaystyle 1 + [g(x)]^2 = 9x^4 + \frac{1}{2} + \frac{1}{144x^4} = \left(3x^2 + \frac{1}{12x^2}\right)^2<br />

    take it from here?
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  3. #3
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    Thanks a lot! I got the answer, but I'm just curious as to how the -(1/2) appears when you square, and disappears again when you simplify... sorry I'm probably missing something obvious here haha
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  4. #4
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    Quote Originally Posted by strawlion View Post
    Thanks a lot! I got the answer, but I'm just curious as to how the -(1/2) appears when you square, and disappears again when you simplify... sorry I'm probably missing something obvious here haha
    basic algebra ... (a-b)^2 = a^2 - 2ab + b^2

    add the 1 ...

    a^2 + 2ab + b^2 = (a+b)^2

    ... work on it.
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