Exploiting Symmetry: Integration Problem from 1987 Putnam B1

Описание: Let's make two intuitive substitutions with regard to symmetry to discover a quick and elegant solution.

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Reference:
"The William Lowell Putnam Mathematical Competition (1985-2000)" by Kiran S. Kedlaya, Bjorn Poonen, and Ravi Vakil; published by the Mathematical Association of America in 2002.