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

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Mathematics · Calculus of Variations

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

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y(x) = 115(x4 + 14) is an extremal for J3

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Answer 1

y(x) = 12(x2 - x + 2) is an extremal for J1

Answer 2

y(x) = x is an extremal for J0

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Answer 4

y(x) = 115(x4 + 14) is an extremal for J3

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

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

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