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Calculus
${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
Fundamental theorem Limits Continuity Rolle's theorem Mean value theorem Inverse function theorem
Differential Definitions Derivative (generalizations) Differential infinitesimal of a function total Concepts Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem Rules and identities Sum Product Chain Power Quotient L'Hôpital's rule Inverse General Leibniz Faà di Bruno's formula Reynolds
Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann integral Lebesgue integration Contour integration Integral of inverse functions Integration by Parts Discs Cylindrical shells Substitution (trigonometric, tangent half-angle, Euler) Euler's formula Partial fractions (Heaviside's method) Changing order Reduction formulae Differentiating under the integral sign Risch algorithm
Series Geometric (arithmetico-geometric) Harmonic Alternating Power Binomial Taylor Convergence tests Summand limit (term test) Ratio Root Integral Direct comparison Limit comparison Alternating series Cauchy condensation Dirichlet Abel
Vector Gradient Divergence Curl Laplacian Directional derivative Identities Theorems Gradient Green's Stokes' Divergence generalized Stokes Helmholtz decomposition
Multivariable Formalisms Matrix Tensor Exterior Geometric Definitions Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian Hessian
Advanced Calculus on Euclidean space Generalized functions Limit of distributions
Specialized Fractional Malliavin Stochastic Variations
Miscellanea Precalculus History Glossary List of topics Integration Bee Mathematical analysis Nonstandard analysis
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The Integration Bee is an annual integral calculus competition pioneered in 1981 by Andy Bernoff, an applied mathematics student at the Massachusetts Institute of Technology (MIT).^[1][2] Similar contests are administered each year in many universities and colleges across the United States and in a number of other countries.

Prospective participants may first need to take a qualifying exam.^[1] The contest is then arranged in a manner similar to a sports tournament, with those who incorrectly evaluate integrals after a certain number of trials are eliminated. Constants of integration may be ignored, but the final answer must be in reduced form and in terms of the original variable.^[3] At some institutions, such as MIT, contestants will evaluate assigned integrals on a chalkboard in front of the audience.^[4] In some others, such as the University of Connecticut, they may do so in their seats on paper.^[3] Contestants may either be all students from the hosting institution (such as MIT or the University of California, Berkeley),^[5][6] undergraduates only (such as at the University of Connecticut),^[3] or undergraduates and high-school students (such as at the University of North Texas),^[7] or all university students as well as high school students from the same area (such as West Virginia University).^[8] At the University of Dayton (Ohio), students compete in teams of two.^[9]

Participants are expected to be familiar with the standard methods of integration.^[7]

Integration Bee contests continue to be held at MIT, with the champion awarded a hat carrying the title, "Grand Integrator."^[4] Integration Bee contests are now regularly conducted in major American colleges and universities.

In the South, they are the University of Florida,^[10] Florida Polytechnic University,^[11] West Virginia University,^[8] Louisiana Tech University,^[12] and the University of North Texas.^[7]

In the Northeast, they are the University of Scranton,^[13] Connecticut College,^[14] Central Connecticut State University,^[15] Columbia University,^[16] and the State University of New York.^[17]

In the Midwest, they are the University of Wisconsin–Madison,^[18] Prairie State College (Illinois),^[19] the University of Illinois at Urbana–Champaign,^[20] and the University of Dayton (Ohio).^[9]

In the West, they are Brigham Young University, Utah Valley University,^[21] Fresno State University,^[22] Cosumnes River College,^[23] the University of California, Berkeley,^[6] various other institutions in California,^[24] and Oregon State University.^[25]

The Louisiana/Mississippi chapter of the Mathematical Association of America is responsible for holding the Integration Bee in these two states^[26] and the American Mathematical Society at the University of Connecticut.^[3]

A Philippine integration competition (often shortened as Integ Bee) was originally held four times at the University of the Philippines Diliman, located in Quezon City, and sponsored by UP Physics Association (UPPA). Subsequently, the competition was scaled up to allow undergraduates of other Philippine universities to participate.^[27] One typical event in 2014 at the Philippine National Institute of Physics, allowed contestants to test their accuracy and speed, capability in mental solving, and mastery in evaluating integrals.^[27] The winner received a cash prize of 5,000 Philippine pesos (about €100 or US$113), whilst two runners-up received 1,000 pesos (about €20 or US$22).^[27]

In the United Kingdom, the Integration Bee is held at the University of Cambridge,^[28] which welcomes participants from other British universities, including University of Oxford, Imperial College London, Durham University and University of Warwick. Elsewhere in the English-speaking world, the contest is held at the University of New South Wales, Australia,^[29] and the Indian Institute of Science Education and Research, Pune.^[30]

In Poland, the Integration Bee is adopted at University of Warsaw, with the name The Grand Integration Tournament UW (pol. Wielki Turniej Całkowania UW). It has been organised annually since 2022 by three Faculty Student Councils (Mathematics, Physics and MISMaP). The running traditions are 3D printed medals for 1st, 2nd and 3rd place, which are printed by Faculty of Physics UW in Makerspace@UW, and the use of Hagoromo chalk.

In Switzerland, the Integration Bee was held at the École Polytechnique Fédérale de Lausanne for the first time in 2023.

In Austria, the Integration Bee Vienna was organized for the first time by two students Maksym Czarniecki & Samuel Krech in May 2024 and hosted at the faculty of mathematics of the University of Vienna.^[31]

In Germany, there have been various events in the style of an Integration Bee. For example, the University of Bonn held the Integration Bee for the first time in November 2024.^[32]

In Bangladesh, Chittagong University of Engineering & Technology (CUET) made history by organizing the country's first-ever Integration Bee competition in November 2024. The event featured two stages: an initial written round^[33] followed by a series of one-on-one matches. From the written round, 16 students advanced to compete in 1v1 duels, resulting in eight matches before the quarterfinals. The competition then progressed through the quarterfinals, semifinals, and a final match, with an additional match held to determine the second runner-up. The CUET Schrödinger Society, in collaboration with the Department of Mathematics, honored the top three participants, including the "Grand Integrator," with custom-designed metal crests and medals. All 16 finalists received uniquely crafted medals, and the top three winners were awarded prize money as part of the recognition for their achievements. The event was live-streamed on the official Facebook page of the CUET Integration Bee, allowing a wider audience to witness this innovative academic competition.

In Egypt, three integration bees were held in 2023. The first one was held by the Department of Mathematics at Cairo University in April. The second was held by the Department of Engineering of the same school; this event was open to freshmen only. The third was held in the Zewail City of Science, Technology and Innovation.^{[citation needed]}

While integral calculus is no longer an actively researched topic in mathematics, there is some correlation between success in the integration bee and success in other areas of mathematics. On a more individual level the winners of the integration bee are held in high honor by their colleagues and professors alike.^[4]

• List of mathematics competitions
• Math circle
• Mathematics education in the United States
• William Lowell Putnam Mathematical Competition

• Integration Bee website
• Facebook page of the Integration Bee
• On-line portal, UP Physics Association
• Twitter account, UP Physics Association
• Integration Bee Austria (Vienna) website