For α ≥ 0, consider the functional: Jα[y] = ∫12 (y')2xα dx defined for all continuously differentiable functions on the interval [1, 2] satisfying y(1) = 1, y(2) = 2. Which of the following statements is true?

Question

Mathematics · Calculus of Variations

Verified Solution4 Options

Answer 1

y(x) = x2 - x + 22 is an extremal for J1

Answer 2

y(x) = x is an extremal for J0

Answer 3

y(x) = x2 + 23 is an extremal for J1

Answer 4

y(x) = x4 + 1415 is an extremal for J3

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