# 2013 MIT Integration Bee

The webpage for this year's contest, held in January of 2014, is available here.

## Overview

Integration is one of the core constructions in modern mathematics. It is attached to famous names such as Newton, Leibnitz, Riemann, Lebesgue, Stieltjes, Wiener, ItÃ´, 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.

MIT has held an annual integration bee since 1981. 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 to the main event to cheer on MIT's best speed-integration specialists, and watch them vie for the coveted title of Grand Integrator!

## Results

The qualifying round integrals are available here. The qualifiers for the 2013 integration bee are listed below in alphabetical order.

• Justin Brereton
• Aaron Brookner
• Whan Ghang
• Benjamin Gunby
• Diptarka Hait
• Ben Kraft
• Mitchell Lee
• Gabriel Lesnick
• Carl Lian
• Rodrigo Paniza
• Jon Schneider
• Sayeed Tasnim
• Forest Tong
• Wuttisak Trongsiriwat
• Ray Hua Wu
Congratulations to this year's Grand Integrator Justin Brereton and runner-up Carl Lian.

## Example Integrals

Here are some integrals from last year's bee.
 Easier $$\displaystyle{\int x^{1/4}\log(x)\,dx}$$ $$\displaystyle{\int\frac{\sec(\log(x))}{x}\,dx}$$ Medium $$\displaystyle{\int\frac{x}{(2-x)^3}\,dx}$$ $$\displaystyle{\int_0^{\pi^2/4} \sin(\sqrt{x})\,dx}$$ Harder $$\displaystyle{\int \frac{169\sin(x)}{5\sin(x)+12\cos(x)}\,dx}$$ $$\displaystyle{\int x\sqrt{\frac{1-x^2}{1+x^2}}\,dx}$$

See last year's integration bee website for more examples.

## Prizes

The final eight will receive gift certificates to Toscanini's ice cream, and the final two competitors will receive book prizes.

## Organizers

Zachary Abel and Samuel Watson were the organizers for the 2013 integration bee.