# Solution: 2010-13 Upper bound

Prove that there is a constant C such that

$$\displaystyle \sup_{A<B} \int_A^B \sin(x^2+ yx) \, dx \le C$$

for all y.

The  best solution was submitted by Minjae Park (박민재), KSA (한국과학영재학교)  3학년. Congratulations!

Here is his Solution of Problem 2010-13.

Alternative solutions were submitted by 정진명 (수리과학과 2007학번, +3), 정성구 (수리과학과 2007학번, +3), 심규석 (수리과학과 2007학번, +3). Three incorrect solutions were submitted (서**, 정**, Ver**).

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## 2 thoughts on “Solution: 2010-13 Upper bound”

1. Minjae Park

There’s a typo mistake. In the third line of 5th page,
R≤0 should be R≥0 (the direction of inequality should be changed.)

2. Anonymous

There’s a typo mistake. In the third line of 5th page,
R≤0 should be R≥0 (the direction of inequality should be changed.)

There’s a typo mistake. In the third line of 5th page,
R≤0 should be R≥0 (the direction of inequality should be changed.)