[quote=&quot;Massimo Gobbino&quot;:p91u4hzw]where [latex:p91u4hzw]v&#40;x&#41;[/latex:p91u4hzw] is any function that is zero at the boundary and satisfies

[latex:p91u4hzw]\displaystyle\int_0^\pi\left&#40;\cos x\cdot v&#39;&#40;x&#41;-\sin x\cdot v&#40;x&#41;\right&#41;\,dx\neq 0[/latex:p91u4hzw].

It should not be difficult to show the existence of such a [latex:p91u4hzw]v&#40;x&#41;[/latex:p91u4hzw][/quote:p91u4hzw]

This is not true ... the integral is always 0 because it is a Null Lagrangian ...