Integration Bee

Annual integral calculus competition

Finalists of the 2006 MIT Integration Bee, with the "Grand Integrator" in the middle.Part of a series of articles about

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∫ a b f ′ ( t ) d t = f ( b ) − f ( a ) {\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}

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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.

## Rules and conventions

[edit]

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]

## U.S. competitions

[edit]

Viewers and participants of the 2020 Berkeley Integration Bee

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]

## Non-U.S. competitions

[edit]

### Africa

[edit]

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]

### Asia

[edit]

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]

CUET Integration Bee 2024 Grand Finale

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[28] 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.

### Europe

[edit]

In the United Kingdom, the Integration Bee is held at the University of Cambridge,[29] 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,[30] and the Indian Institute of Science Education and Research, Pune.[31]

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.[32]

In Germany, there have been various events in the style of an Integration Bee. In 2024, both Heidelberg University and the University of Bonn held their first competitions, in May and November, respectively.[33][34]

In Barcelona (Catalonia, Spain), the Integration Bee takes place at Polytechnic University of Catalonia, inside the Maths and Statistics Faculty (FME). Since 2023, the contest is held around the start or May.[35] All editions have counted with more than 50 participants.

In Lisbon, Portugal, the Integration Bee was organized for the first time in 2025 at Instituto Superior Técnico (IST) - Universidade de Lisboa, and adopted a format that allowed students to participate individually or in pairs. [36]

## Impact

[edit]

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]

## See also

[edit]

* Education portal
* Mathematics portal

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

## References

[edit]

1. ^ a b Watson, Samuel. "2014 MIT Integration Bee". Retrieved June 18, 2023.
2. ^ Mihori, Jim (January 29, 1981). "Integration Bee". The Tech. Vol. 100, no. 58. Retrieved June 18, 2023.
3. ^ a b c d "Integration Bee". AMS Student Chapter, University of Connecticut. 2018. Retrieved February 6, 2021.
4. ^ a b c Baker, Billy (January 20, 2012). "An integral part of MIT life". Boston Globe. Retrieved February 6, 2021.
5. ^ "41st Annual MIT Integration Bee". Integration Bee. Massachusetts Institute of Technology. 2022. Retrieved April 9, 2022.
6. ^ a b "Integration Bee". Berkeley SPS. University of California, Berkeley. Retrieved February 6, 2021.
7. ^ a b c "Integration Bee". College of Science, Department of Mathematics, University of North Texas. 2020. Retrieved February 6, 2021.
8. ^ a b "WVU Integration Bee Competition". School of Mathematical and Data Sciences, West Virginia University. 2023. Retrieved May 4, 2023.
9. ^ a b "An Integration Celebration for UD Undergraduates". University of Dayton College of Arts and Sciences. 2020. Retrieved May 4, 2023.
10. ^ "2015 University of Florida Integration Bee". March 14, 2014. Retrieved June 18, 2023.
11. ^ "Integral Bee Competition". 2019. Retrieved June 18, 2023.
12. ^ McKnight, Brandy (February 10, 2017). "Inaugural Integration Bee showcases students' mathematics skills". Louisiana Tech University. Retrieved February 6, 2021.
13. ^ "Seventh annual integration bee". April 30, 2014. Retrieved June 18, 2023.
14. ^ "Four honored with College's highest faculty awards". Connecticut College. May 11, 2017. Retrieved February 6, 2021.
15. ^ "Integration Bee". Mathematics. Central Connecticut State University. 2019. Retrieved February 6, 2021.
16. ^ Dragomir, George (2023). "Columbia Integration Bee Contest Information". Github. Retrieved January 26, 2023.
17. ^ Integration Bees Past and Present Archived 2015-01-26 at the Wayback Machine, State University of New York, New Paltz
18. ^ Reardon, Jim (May 8, 2012). "University of Wisconsin Integration Bee". University of Wisconsin-Madison Physics. Retrieved February 6, 2021.
19. ^ "Integration Bee". Mathematics. Prairie State College. Retrieved February 6, 2021.
20. ^ Hari, Shyam (February 23, 2020). "Second Edition! Integration Bee 2020". Illinois Integration Bee. University of Illinois at Urbana-Champaign. Retrieved February 6, 2021.
21. ^ "Integration Bee Results". Mathematics Department, Brigham Young University. 2019. Retrieved February 6, 2021.
22. ^ "Twelfth Annual Fresno State Integration Bee". Archived from the original on 2015-02-19. Retrieved 2014-03-05.
23. ^ Lee, Jared (May 3, 2017). "Students competed in math competition to exercise their skills". The CRC Connection. Retrieved February 6, 2021.
24. ^ Hartland, Tucker (May 23, 2019). "SIAM Student Chapter Conference Unites Valley Regional Applied Mathematics Community". University of California Merced News Room. Retrieved February 6, 2021.
25. ^ "Pi Week: Integration Bee". College of Science, Oregon State University. 2020. Retrieved February 6, 2021.
26. ^ Evans, Chrystal (March 16, 2018). "Denham Springs student places third in Mathematical Association of America competition". The Living Parish News. Retrieved February 6, 2021.
27. ^ a b c "Integration Bee 2014: Into the Galaxy — first speed integration contest in Metropolitan Manila". February 28, 2014. Retrieved June 18, 2023.
28. ^ Aslam, Habib (2024-11-20). "চুয়েট ইন্টিগ্রেশন বি এর বাছাইপর্ব অনুষ্ঠিত". চুয়েট নিউজ২৪. Retrieved 2024-11-24.
29. ^ "UK Integration Bee". MathSoc. Archimedean Society, Cambridge. Retrieved July 15, 2023.
30. ^ "Integration Bee Champions". MathSoc. University of New South Wales. Archived from the original on October 17, 2021. Retrieved February 6, 2021.
31. ^ Khan, Ashwin (March 8, 2017). "The numbers game". Pune Mirror. Archived from the original on October 21, 2021. Retrieved February 6, 2021.
32. ^ "Integration Bee Vienna". Retrieved May 30, 2024.
33. ^ "Heidelberg Integration Bee". Retrieved April 4, 2025.
34. ^ "Integration Bee Bonn". Retrieved November 9, 2024.
35. ^ "Heidelberg Integration Bee". Retrieved April 9, 2025.
36. ^ "IST Integration Bee". Retrieved June 2, 2025.

## External links

[edit]

* 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

* v
* t
* e

Integrals

Types of
integrals|

* Riemann integral
* Lebesgue integral
* Burkill integral
* Bochner integral
* Daniell integral
* Darboux integral
* Henstock–Kurzweil integral
* Haar integral
* Hellinger integral
* Khinchin integral
* Kolmogorov integral
* Lebesgue–Stieltjes integral
* Pettis integral
* Pfeffer integral
* Riemann–Stieltjes integral
* Regulated integral

Integration
techniques|

* Substitution
* Trigonometric
* Euler
* Weierstrass
* By parts
* Partial fractions
* Euler's formula
* Inverse functions
* Changing order
* Reduction formulas
* Parametric derivatives
* Differentiation under the integral sign
* Laplace transform
* Contour integration
* Laplace's method
* Numerical integration
* Simpson's rule
* Trapezoidal rule
* Risch algorithm

Improper integrals|

* Gaussian integral
* Dirichlet integral
* Fermi–Dirac integral
* complete
* incomplete
* Bose–Einstein integral
* Frullani integral
* Common integrals in quantum field theory

Stochastic integrals|

* Itô integral
* Russo–Vallois integral
* Stratonovich integral
* Skorokhod integral

Miscellaneous|

* Basel problem
* Euler–Maclaurin formula
* Gabriel's horn
* Integration Bee
* Proof that 22/7 exceeds π
* Volumes
* Washers
* Shells

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