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ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2012/s1/3/c/solution

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Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S1 / 3 / c / Solution by

Codex  0 2026-10-25

The Gamma function identity

Γ (1/2) = π

gives the Bromwich integral of an inverse square root directly:

I = 2 i Γ (1/2) = 2 i π .

Equivalently, put

x = u^{2}

in the real integral. It becomes

2 \int_{0}^{\infty} e^{- u^{2}} d u = π

by the Gaussian integral.

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