Integration is one of the core constructions in modern mathematics. It is attached to famous names such as Newton, Leibnitz, Riemann, Lebesgue, Stieltjes, Wiener, Itô, Stratonovich, Skorohod, and many others. By definition, the integral of a (nice) function is the area of the region bounded below the graph of that function. The Fundamental Theorem of Calculus (the cornerstone of calculus, as taught, for example, in 18.01) allows the calculation of integrals using another key calculus ingredient - differentiation - *in reverse*. While differentiation is completely routine, applying it backward to integrate requires skill and creativity.

For many years (though probably less than 128), MIT has held the world's most prestigious (and first) Integration Bee. The format has varied, ranging from a traditional round-robin to an NHL-style playoff tournament. Each year the bee draws a large crowd. Come cheer on MIT's best
speed-integration specialists, and watch them vie for the coveted title **Grand Integrator**!

This year's finalists, ranked in order of their performance on the qualifying test, are:

- Aaron Brookner
- Praveen Venkataramana
- Qian Yu
- Andrew Jeanguenat
- Dennis Tseng
- Carl Lian
- Polnop Samutpraphoot
- Jonathan Schneider
- Benjamin Kraft
- Leon Zhang
- Ben Bond
- Justin Brereton
- Jacob Hurwitz
- Kate Rudolph
- Yi Sun
- Melih Ucer

Update: Here are the questions and answers for the qualifying round.

The integration bee is a four round seeded tournament, with pairing progression detailed on the diagram below. The first round will be a

In the second round, the first round winners compete in

The integrals will become slightly more challenging as the contest progresses to higher rounds. All integrals in any given round will be at approximately the same level of difficulty, none trivial. The time allotted for these integrals will be: 1 minute each for the first round, 2 minutes each for the second round, 3 minutes each for the third round, and 4 minutes each for the final round. If neither contestant gives a correct solution within the allotted time, both start with a new integral. When a competitor

Here are some fun integrals from last year's tournament.

The final eight will receive gift certificates to Toscanini's ice cream. The final two competitors will receive book prizes, and the winner of the championship round will be crowned Grand Integrator.
## UpdateThe Grand Integrator this year isJustin Brereton. The runner-up is Praveen Venkataramana.
Thanks to Sriram Krishnan for co-organizing the Bee with me this year (and to the MIT math department for sponsoring it, the prizes and advertising). This year's contest was covered by the Boston Globe. Here is the link to their article. |