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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/9/i/a/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 9 / i / a / Solution by

Codex  0 2026-10-18

The boundary term

[f_{y^{'}} η]_{a}^{b}

vanishes, so stationarity and the fundamental lemma of the calculus of variations give the Euler-Lagrange equation

f_{y} - \frac{d}{d x} f_{y^{'}} = 0.

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