Competition Structure

Top 16 Round (Regular Season):

• Format: 20 integrals in 5 rounds of 4 integral problems, following a Mutually Orthogonal Latin Squares structure, with each contestant attempting one from each round. Four contestants compete at the board per round, and each pair of contestants faces off exactly once. Two minutes are allowed per problem.

• Scoring: A zero-sum scoring system. If P contestants solve a problem and Q fail, solvers earn Q points each, while the failures lose P points each.

  • • For example, if all four contestants solve an easy integral, no points are awarded. If only one contestant solves a difficult integral, that solver earns 3 points while each of the others loses 1 point.

• Advancement: The top 8 contestants with the highest accumulated points advance.

• Ties at the end of the Regular Season are broken in order by:

  • • 1. Number of integrals solved correctly during the Regular Season

    • 2. Sudden Death Elimination

• Estimated Time: The Top 16 Regular Season Round will take approximately 1 hour.

Tie-Breakers (Sudden Death Elimination):

This is only for the Top 8, Top 4, and Top 2 Rounds, and only if needed after each round. Players will play rounds of 1-minute tiebreakers until one integrator is exactly two points ahead of the other. The problems are meant to be easier ones, not requiring heavy computation. It’s more about speed and accuracy.

In each round, two integrators will be at the board solving a problem. If both players get the correct answer, the first to finish wins the point. If one player gets it right, that player earns the point. If neither gets it, no one earns a point. Only the answer written at the end of time counts. If you change your answer midway—your first answer was correct, but your final answer is wrong—you will not earn the point. The correct answer you circle on the board must stay there for the entire duration of the round for it to count. Your final answer should be circled or boxed so that your finish time can be judged accurately.

The problems are designed to be easy, so a tie is usually broken after two or three rounds. However, if after five rounds the score is still tied, or if one integrator is ahead by fewer than two points, we continue until someone earns the next point. From that moment on, the next player to score wins the elimination round, even if the overall score remains tied, since the original “win by two points” rule no longer applies. If after seven rounds no player is ahead, the competitors will settle the elimination round with a best-of-three rock-paper-scissors game.

For example:

• In Round 5, Competitor A has 3 points, and Competitor B has 2 points.

• In Round 6, Competitor B wins the point, making it 3 points tied for both Competitors.

• Because this happened after the 5th round, Competitor B earns the final deciding point and advances, even though the score is tied.

Competition-Specific Rules

1. No notes, calculators, or electronic devices are allowed. All integration formulas and techniques must be memorized or derived.

2. The arbitrary constant (+C) is not required for indefinite integrals.

3. Simplification: Answers must be simplified and clearly presented:

   • • Rational numbers should be fully reduced.

     • Trigonometric functions must be evaluated when possible.

     • Negative exponents are acceptable.

     • You may leave your answer in terms of a substitution, but you must clearly state what the substitution is. A maximum of one substitution is allowed (e.g., you cannot use a w-sub that traces back to a v-sub and then a u-sub). A valid solution, for example, would be writing u2+ln(u)  {u=x2+3x} (The curly brackets are optional, but your answer must clearly indicate the substitution.)

4. Answer Format:

   • • Answers must be in closed form. (no ∑, Π, …, ∫, etc)

     • “Log” refers to the natural logarithm, i.e., ln(...).

     • Nested trig functions must be simplified (e.g., sin(sin⁻¹(x))).

5. Answer Submission: Only the final circled answer will be graded. Incorrect or unclear answers will not be awarded points.

6. Cheating: Spectators and competitors must remain silent. Any attempt to provide assistance to contestants will result in immediate disqualification.

7. Judging: The judge and host reserve the right to determine answer correctness, assign points, and reject excessively complex or egregiously unsimplified solutions (e.g., an unnecessarily long answer when the correct solution is simply 0 or 1).