Variation of an Integral Objective Functional

In the above equation, the coefficient of Sy (i.e., Fy) is called the variational derivative of the functional I with respect to y. Similarly, Fy/ is called the variational derivative of I with respect to y. If F = F y ), then obviously 

Upon substituting 6y = x and the corresponding = — 1 in the above equation and integrating, we obtain 

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