Lecture 1, Part I: Introduction of the Class
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Lecture 1, Part I: Introduction of the Class
MIT 18.642 Topics in Mathematics with Applications in Finance, Fall 2024 Instructors: Vasily Strela, Jake Xia, and Peter Kempthorne View the complete course: https://ocw.mit.edu/courses/18-642-topics-in-mathematics-with-applications-in-finance-fall-2024 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP601Q2jo-J_3raNCMMs6Jves ...
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🔥 Day 138 — 2026 MIT Integration Bee (Qualifying) Q1 Evaluate: ∫ from −pi to pi of sin^(2025)(x) * cos^(2026)(x) dx This looks impossible at first glance, but there’s a 2-second parity trick. Power counts matter: odd vs even makes or breaks symmetry on [−a, a]. 👉 Hints • sin(x) odd → odd^2025 stays odd • cos(x) even → even^2026 stays even • odd * even = odd; integral of odd over [−a, a] is 0 Would you spot the parity in time? ⏱️ 💭 Comment your reasoning below 👇 ✅ Full step-by-step solution i
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