Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007
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Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007
Lecture 01: Derivatives, slope, velocity, rate of change *Note: this video was revised, raising the audio levels. View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
2.7M viewsAug 18, 2009
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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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🔥 Day 138 — 2026 MIT Integration Bee (Qualifying) Q1 Evaluate: ∫ from −pi to pi
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