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4.5 Variational calculus
Problem: Find the strong extrema of the functional: \[ \begin{array}{l} F(x)=\int_{0}^{1}\left(\dot{x}^{2}-x^{2}\right) d t \rightarrow \text { extr }, x(0)=1, \\ x(1)=\cos 1 . \end{array} \]
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