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🔥 Day 145 — 2026 MIT Integration Bee (Qualifying) Q11 Evaluate: ∫ from −1 to 1 of max(0, √(1 − x^2) − 1/2) dx This is a geometry-integral mashup. The integrand is the “height above” the line y = 1/2 under the unit semicircle y = √(1 − x^2). Find where the semicircle is above the line (|x| ≤ √3/2), then integrate √(1 − x^2) and subtract the rectangle area. 👉 Hints • Positive region: |x| ≤ √3/2 • Use ∫ √(1 − x^2) dx = 1/2( x√(1 − x^2) arcsin x ) • Subtract (1/2) · width 📣 Project Mentor: free g
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