# 2014 MIT Integration Bee

## 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, 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.

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 qualifiers for the 2014 integration bee are listed below in alphabetical order.

• Aaron Brookner
• Nachiket Desai
• Eric Fegan
• Neil Gurram
• Diptarka Hait
• Junda Huang
• Ben Kraft
• Kevin Li
• Carl Lian
• Eric Mannes
• Rodrigo Paniza
• Eli Ross
• James Rowan
• Polnop Samutpraphoot
• Sayeed Tasnim
• Jonathan Tidor
• Ray Hua Wu
• Kevin Zhou

## Example Integrals

The 2014 qualifying exam is now available, and here are some integrals from the 2012 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 qualifying round or the 2012 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. The grand prize is the Grand Integrator hat! ## Organizers

This 2014 Integration Bee committee includes John Lesieutre, Ewain Gwynne, and Samuel Watson. We would like to thank Tiankai Liu for contributing integrals.