# 2014 MIT Integration Bee

The next annual MIT Integration Bee will be held in January 2014.

## 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!

## Example Integrals

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 the 2012 integration bee website for more examples.

## Organizers

Please contact Samuel Watson with questions regarding the integration bee.

The webpage for the 2013 contest is available here.