Question

Calculus

2. (20 points.) (Gelfand and Fomin, Calculus of Variations.) Evaluate the functionalderivatives of the following functionals, assuming no variation at the end points.

F[y]=\int_{0}^{1} d x \frac{d y}{d x}

F[y]=\int_{0}^{1} d x y \frac{d y}{d x}

F[y]=\int_{0}^{1} d x x y \frac{d y}{d x}

F[y]=\int_{a}^{b} \frac{d x}{x^{3}}\left(\frac{d y}{d x}\right)^{2}


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