- #1

sap

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- Homework Statement
- given two poles at a distance between them and a rope that it's length is bigger than the distance between them, describe the shape of the rope.

- Relevant Equations
- no relevent equations

i started to think to maybe do an integral to find the minimum area, and then I thought that the area itself is not sufficient because there is more material depending on the slope. so I thought to do an integral depending on the length instead of x.

##dh^{2}=dx^{2}+dy^{2}##

##\int{}f(x)dh= \int{}f(x)\sqrt{dx^{2}+dy^{2}}##

##dy=\frac{dy}{dx}dx=dx f'(x)##

##\int{}f(x)\sqrt{dx^{2}+f'(x)^{2}dx^{2}}=\int{}f(x)\sqrt{f'(x)^{2}+1} dx^{2}##

how can I get a minimum to solvw this question?

##dh^{2}=dx^{2}+dy^{2}##

##\int{}f(x)dh= \int{}f(x)\sqrt{dx^{2}+dy^{2}}##

##dy=\frac{dy}{dx}dx=dx f'(x)##

##\int{}f(x)\sqrt{dx^{2}+f'(x)^{2}dx^{2}}=\int{}f(x)\sqrt{f'(x)^{2}+1} dx^{2}##

how can I get a minimum to solvw this question?