What is the Length Integral Problem at Point (1,1)?

[ankh]

Hi, could someone help me with this problem.

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

Thanks

PS: Is this the right place topost it? I just thought that differentiation is closely connected to integration.

 

[dextercioby]

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

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

Daniel.

 

[Crosson]

More of a calc 2 problem.

The answer is sqrt(x).