For α ≥ 0, consider the functional Jα[y] = ∫12 (y')2/xα dx defined for all continuously differentiable functions defined 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

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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

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Answer 1

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

Answer 2

y(x) = 13(x2 + 2) is an extremal for J0

Answer 3

y(x) = x is an extremal for J2

Answer 4

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

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