Euler Lagrange Equation trough variation

[BasharTeg]

Homework Statement

"Vary the following actions and write down the Euler-Lagrange equations of motion."

Homework Equations

S =\int dt q

The Attempt at a Solution

Someone said there is a weird trick required to solve this but he couldn't remember. If you just vary normally you get \delta S=\int dt \delta q=0
and that's not helpful. Any suggestion on how to avoid this problem?

 

[JHamm]

I believe you need to make your function q = q(t) + \delta q(t) and then observe that since this new function needs to have the same ending points it implies that
<br /> \delta q(t_1) = \delta q(t_2) = 0<br />
And follow that with what \delta S becomes :)

 

[BasharTeg]

thanks but isn't this just the general way of variation?

\delta S = \int dt (f(q+\delta q) - f(q))= \int dt \frac{\partial f}{\partial q} \delta q = \int dt \delta q

and there still the same problem remains that I can't find any function that makes \delta S = 0 for every \delta q because here I would get 1=0.
Or did i miss your point?