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Homework Help: Length of a curve

  1. Mar 19, 2007 #1
    1. The problem statement, all variables and given/known data

    To find the length of the curve defined by y=3x^3+11x from the point (0,0) to the point (1,14), you'd have to compute:

    [tex]\int_{a}^{b} f(x) dx[/tex]

    where a=?, b=? and f(x)=?

    2. Relevant equations

    3. The attempt at a solution

    So I put a to be 0 and b to be 1, since it's asking for the x axis.

    Then I took the equation y=3x^3+11x and got its derivative, 9x^2+11. I subtracted one from the entire equation and square rooted the entire thing, such that it looked like [tex]\sqrt{1-9x^2+11}[/tex].

    Did I do anything wrong here? This is an internet-generated exercise I'm doing.
  2. jcsd
  3. Mar 19, 2007 #2


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    Staff Emeritus
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    Gold Member

    That will give you the area under the curve, not the arc length. Do a bit more searching for the arc lenght forumal.
  4. Mar 19, 2007 #3
    That will not give you the area under the curve, nor will it give you the arc length!

    The arc length would [tex]S = \int_a^b \sqrt{1 + (\frac{dy}{dx})^2}[/tex]

    *Note that is (dy/dx)^2, I did something latex didn't like.
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