Integration Bee

Every winter semester TRU Math Club together with the Department of Mathematics organize a contest to challenge students’ skills in evaluating integrals – Integration Bee.  


The contest consists of elimination rounds in which contestants find antiderivatives of given functions. As the contest progresses, functions increase in complexity.

  • In case there are more than 16 people registered, there is a qualification round. All participants get list of integrals and a time limit. 16 people who solve the most integrals get into the first round. 
  • Pairs get formed arbitrary among the 2^(5-n) students of the n-th round. Every pair gets called to the board and an integral is given to students. If a student has an answer, they have to circle it and if it is correct – they win the round and the second person gets eliminated. In case of a wrong answer, opponent has the remaining time to get an answer. In case neither of students solved it, they are given a new integral and a new time limit. 
  • All integrals in the first round will be just checking the knowledge of the basic techniques of integration and are supposed to be solved in 2 minutes. Second round includes tricks and the time limit is 3 minutes. Third round – 3 or 4 minutes. During the final round students might have 4 or 5 minutes to solve an integral. Time might be adjusted by the jury depending on the complexity of integrals and students anticipation. 
  • Students of Math 1230, 1240 and 1250, who get into Top-3 get extra points to their grade (not promised every year)
  • Competition can get extended to 4 rounds

Basic techniques:

  • Integrals of powers and of trigonometric functions
  • Substitution
  • Integration by parts
  • Partial fraction decomposition
  • Trigonometric substitutions

Tricky stuff:

  • Integrals of powers of trigonometric functions.
  • Integrals of hyperbolic functions.
  • Completing the square.
  • Elimination of radicals by substitution.
  • Substituting the tangent of a half-angle.
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