Suppose that \( f: [a, b] \to \mathbb{R} \) is a smooth, convex function, and there exists a constant \( t>0 \) such that \( f'(x) \geq t \) for all \( x \in (a, b) \). Prove that
\[
\left| \int_a^b e^{i f(x)} dx \right| \leq \frac{2}{t}.
\]

The best solution was submitted by Anar Rzayev (KAIST 전산학부 19학번, +4). Congratulations!

Here is the best solution of problem 2023-07.

Other solutions were submitted by 김찬우 (연세대학교 수학과 22학번, +3), 박기윤 (KAIST 새내기과정학부 23학번, +3), 박준성 (KAIST 수리과학과 석박통합과정 22학번, +3), 오현섭 (KAIST 수리과학과 박사과정 21학번, +3), 이명규 (KAIST 전산학과 20학번, +3), 최예준 (서울과학기술대학교 행정학과 21학번, +3), Matthew Seok (+3), James Hamilton Clerk (+3).