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## Seventh Annual Integration Bee

### Wednesday, April 30, 2014

An Integration Bee is like a spelling bee but contestants find antiderivatives of functions of a single real variable. The contest consists of a high school and a college division. Everyone making it to the Final Round will win $25, and the winner of each division’s Final Round will be crowned the division’s Integration Champion and will win a total of $100!

Questions? Contact Dr. Stacey Muir.

### Program

The Bee will be held in the DeNaples Centers Ballroom (fourth floor). For directions, click here.

- 4:30 – 4:45 pm
- Sign in and review the rules
- 4:45 – 5:15 pm
- First Round: Definite Integration Competition
- 5:15 – 6:00 pm
- Dinner*
- 5:45 – 6:00 pm
- Raffle prizes and certificates of participation will be awarded
- 6:00 – 7:30 pm
- Final Round: Indefinite Integration Bee

* Faculty and chaperones are welcome but not required. Please email Dr. Stacey Muir to add faculty and chaperones to the dinner.

### SPONSORS

Maplesoft

American Mathematical Society

The University of Scranton Office of Admissions

## Registration

Registration is free, but you must register below by Tuesday, April 22 in order to participate in the Integration Bee. Contact Dr. Stacey Muir if you need to cancel your registration.

Faculty and chaperones are welcome but not required. They need not register below but should email Dr. Stacey Muir to be added to the dinner.

## Rules

No electronic devices (e.g. calculators, phones, etc.), printed materials, or notes will be allowed during the competition. We will supply scratch paper. There will be a high school and a college division. Each will abide by the following rules.

### Round One: Definite Integration Competition

During Round One, participants in each division will be evaluating the same definite integrals. Each participant will be given an answer sheet and will have a given time (approximately 2 minutes*) to complete a definite integral. Each definite integral will be displayed on a screen. By the end of the given time, participants must write a simplified answer on the answer sheet to be considered for correctness. At the end of the given time, all hands must go up and judges will grade the result immediately. It is at the discretion of the judges to disqualify an answer not written before the given time is over. We anticipate having a displayed countdown timer and, if not, we will make announcements as the end of the time approaches. This will repeat for approximately 15 definite integrals. For each correct answer, participants will receive one raffle ticket to be entered for prizes to be drawn after dinner.

Five participants in each category will advance to the Final Round. Those moving on will be determined by the total number of correct definite integrals. Each definite integral will be weighted though. Only in the event of a tie for the cutoff score for the Final Round will the weights be used to break the ties with those earning a higher weighted score moving on. If after this, there is still a tie for the cutoff score, we will use a second tiebreaker (explained below) for all participants at the cutoff score. Everyone moving into the Final Round will receive $25.

### Tiebreaker

A Tiebreaker round will be completed separately from 5:30 – 5:45 pm as needed. All participants remaining in the tiebreaker will be required to complete the same indefinite integral in a given time. At the end of the time, if the number of those answering correctly is larger than the minimum number of spots and smaller than the maximum number of spots left available to advance to the Final Round, they will move on and the tiebreaker is over. If the number of those answering correctly exceeds the maximum number to advance, all those answering correctly will continue to the next tiebreaker problem. If the number of those answering correctly is fewer than the minimum to go on, they will advance to the Final Round and all those answering incorrectly will continue to the next tiebreaker problem.

### Final Round: Indefinite Integration Bee

This part of the competition will be conducted in rounds. Each contestant remaining at the beginning of a round will attempt an integral in a given amount of time one at a time.

Contestants will be given an indefinite integral one at a time to be attempted on a whiteboard or chalkboard in a given amount of time (approximately 1 – 3 minutes*). If a contestant answers correctly before time expires, the contestant remains in the competition. Once every remaining contestant has attempted one problem, a round is completed. If during any round, all contestants are unable to complete the problem correctly in the time allotted, all contestants will remain in the competition for another round. The last person remaining wins an additional $75 and will be crowned the Integration Champion!

* The details on the exact time given to complete an integral will be announced during the introduction and review of rules at the beginning of the competition.

## Integrals

### Previous Integration Bee Problems

- 2013 High School Round One
- 2013 High School Final Round
- 2012 High School Round One
- 2012 High School Final Round

The countdown timer used in these files functions properly only on select pdf readers, e.g., PDF-XChange Viewer works.

### Types of Integrals

Integrands will only be real-valued functions of a single variable. The organizers will have full discretion as to what integrals will be issued throughout the contest and to the correctness of the answer.

The integration techniques or integrands that may be employed for the high school division are

- power functions
- trigonometric functions
- exponential functions
*u*-substitution- integration by parts

The integration techniques that may be employed for the college division include all of those listed above and

- powers of trigonometric functions
- trigonometric substitution
- partial fraction decomposition

During the Final Round, arbitrary constants will not be considered in the evaluation.