# Extremals - calc of variations

by jordan23
Tags: calc, extremals, variations
 P: 3 I am trying to find the extremal that minimizes $$\int_{0}^{1} \sqrt{y(1+y'^2)} dx$$ Because it is not explicitly a function of the free variable x, I can use the shortcut: constant=F-y'*(dF/dy') to solve for y(x) My problem is that after grinding through the algebra my y(x) is a function of itself, in other words I cannot isolate the variable I want to. If anybody can offer some tips on either another way to go about this problem or maybe argue that y(x) can be isolated it would be greatly appreciated. Thanks in advance for the help! (In case the formatting doesn't work, everything inside the integral is raised to the 1/2)
 P: 80 Won't you get the same answer if you extremize $$\int_0^1y(1+y'^2)dx$$ instead? dhris