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Kidphysics
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Homework Statement
Path between O=(0,0) and P=(0,4) for which the integral
int. O to P (x (1-y'^2))^(1/2) dx
becomes stationary.
Homework Equations
http://en.wikipedia.org/wiki/Calculus_of_variations#Example
The Attempt at a Solution
Okay guys,
so mimicking the example from wiki but with L= (x)^1/2 (1-y'^2)^1/2
dL/dy=0 and dL/dy'= -(x)^1/2 y' / (1-y'^2)^1/2 and then d/dx dL/df' = - y'/[(2x^1/2)(1-y'^2)^1/2]
and since d/dx dL/df' =0 this implies y'=0 and we integrate to get y=c, adhering to boundary conditions y must equal 0... was that the correct way sorry for not writing in latex if I must I will redo the post