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The winning integral at Tuesday’s Integration Bee, evaluated by Justin T. Brereton ’13 in two minutes. Hint: consider inverse functions.
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Course 18 senior Justin Brereton is Grand Integrator again

Around 70 people gathered last night in 10-250 to watch 15 students duke it out at MIT’s Integration Bee.

Furrowed brows betrayed the intensity of the contest, but participants kept the tone friendly, explaining solutions to each other even after they were eliminated. After two hours, only Carl F. Lian ‘15 and Justin T. Brereton ‘13 remained. Armed with chalk and board, the two vied for the prize hat, embroidered with an integral sign.

“Aw, shit,” Lian said to himself, not for the first time that night, as he attempted to solve one of the final round’s integrals before Brereton. The same integral had appeared earlier, but with limits. Using a geometric approach that evaded the others, Lian had evaluated the definite version in seconds, much to the delight of the audience. But the indefinite counterpart bested both finalists.

Lian went on to bring the score to 2-0, but Brereton followed with two wins in a row, leaving them neck and neck for the game point.

The last problem was a peculiar definite integral involving a base-2 logarithm. Lian wasn’t making much progress, but 28 seconds in, Brereton boxed his answer, 1, with no other work than some mystical squiggles. (For this integral, there would be no repeat of the kerfuffle earlier over whether an answer was completely simplified.) Then, with two minutes left, Brereton changed his answer to 2. A round of giggles was followed by a round of applause when he was revealed to be correct, earning defending champion Brereton the 2013 title.

—Leon Lin