Part CCSIR NET June 2024free-endpoints-make-it-a-distance

Free endpoints make it a distance

The infimum of the set { $\int_{a}$ ᵇ $1 + (y^{'} (t))^{2}$ dt : $y \in C^{1} [a, b], y (a) = a^{2}, y (b) = b - 5$ } is

A. $192 /8$ ✓
B. $192$
C.19/8
D. $19/ (22)$

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.

50 are analysed free — try those first.

Related counterexample: A weak minimum of a functional is a strong minimum

More on this topic

null lagrangian termJune 2023
coupled euler lagrangeJune 2023
Part C questionDecember 2023
weak vs strong extremumDecember 2023
a total derivative term cannot affect the extremalDecember 2024
small values permit large slopesDecember 2024

The chapter behind this: Euler–Lagrange, first integrals and null Lagrangians — free to read

From Calculus of Variations › Euler–Lagrange equation and standard functionals

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