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Length Integral Problem

  1. Jan 9, 2005 #1
    Hi, could someone help me with this problem.

    Find a curve through the point (1,1) whose length integral is
    [itex] L = \int_{1}^{4} \sqrt{1+ \frac {1} {4x}} dx [/itex]


    PS: Is this the right place topost it? I just thought that differentiation is closely connected to integration.
  2. jcsd
  3. Jan 9, 2005 #2


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    The line integral of the first kind giving the length of the curve C is
    [tex] L(C)=:\int_{C} dl [/tex](1)

    If the curve "C" is given through the explicit equation
    [tex] y=y(x) [/tex](2)
    ,it can be shown that the formula (1) becomes this Riemann integral
    [tex] L(C)=\int_{x_{1}}^{x_{2}} \sqrt{1+(\frac{dy(x)}{dx})^{2}} dx [/tex](3)

    Make the analogy between (3) and your formula to find a first order LODE with separable varaibles.

    So your posting the problem in the "Diff.eq." subforum was correct... :smile:

  4. Jan 15, 2005 #3
    More of a calc 2 problem.

    The answer is sqrt(x).
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