Peyam goes PUTNAM: Destroying a Monster Polar Integral (2021 Putnam A4)

Peyam goes Putnam: Destroying a monster polar integral. Calculating a hard math competition integral that appeared on the 2021 William Lowell Putnam Exam A4, using calculus techniques such as polar coordinates, averages, change of variables and jacobians, rotations, weierstrass substitution, and inverse trig substitution. In simplest terms, the question is: What is the limit of the integral as the radius of the domain goes to 0. Watch a math professor get destroyed by this seemingly innocent integral. Can you handle the math heat?

0:00 The Integral
3:30 Rotation
6:00 Cleaning this up
9:50 Polar polar polar
18:50 Weierstrasssssssssssss
22:50 The answer

Big thanks goes to Kiran Kedlaya, for maintaining his Putnam exam webpage: https://kskedlaya.org/putnam-archive/

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