Calculus of variations is a subject where you study the extrema (maximum or minimum) of a function of functions.
We know that, to find the extrema (maximum or minimum) of a “functional” of the form
![v[f(x)]=\int_a^b F(x,f(x),f'(x))dx; f(a)=f_1,f(b)=f_2](https://s0.wp.com/latex.php?latex=v%5Bf%28x%29%5D%3D%5Cint_a%5Eb+F%28x%2Cf%28x%29%2Cf%27%28x%29%29dx%3B+f%28a%29%3Df_1%2Cf%28b%29%3Df_2&bg=ffffff&fg=6a6c6e&s=0&c=20201002)
we first identify and substitute 
to obtain a Ordinary Differential Equation, solving which gives the extrema we are looking for, making use of the boundary conditions.
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Mathematicos 