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Part BCSIR NET December 2023

Isoperimetric problems

The cardinality of the set of extremals of J[y]=∫01(y′)2J[y] = \int_{0}^{1} (y')^{2} dx subject to y(0)=1,y(1)=6,∫01yy(0) = 1, y(1) = 6, \int_{0}^{1} y dx = 3 is

  1. A.0
  2. B.1✓ Correct
  3. C.2
  4. D.countably infinite

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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More on this topic

The chapter behind this: Constrained variational problems — free to read

From Calculus of Variations › Isoperimetric problems

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