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(Solved): Solve the problem of finding the curve of shortest length connecting the points \( (a, \alpha) \) ...
Solve the problem of finding the curve of shortest length connecting the points \( (a, \alpha) \) to \( (b, \beta) \), which is given by: \[ \min _{x} \int_{a}^{b} \sqrt{1+\dot{x}^{2}} d t \] subject to \[ x(a)=\alpha, x(b)=\beta . \]