Prove or disprove that for all positive integers \(m\) and \(n\), \[ f(m,n)=\frac{2^{3(m+n)-\frac12} }{{\pi}} \int_0^{\pi/2} \sin^{ 2n – \frac12 }\theta \cdot \cos^{2m+\frac12}\theta \, d\theta\] is an integer.
The best solution was submitted by 김경석 (경기과학고등학교 3학년). Congratulations!
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Alternative solutions were submitted by 이병학 (2013학번, +2), 박훈민 (2013학번, +2), 배형진 (공항중학교 3학년, +2). One incorrect solution was submitted (LSC).
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