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