Intervals and integrals, an integral involving the floor function. Try integrals like this one everyday at dailyintegral.com #math #mathematics #integral #calculus #foryoupage
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🔥 Day 128 — 2025 MIT Integration Bee (Qualifying) Q11 Evaluate: Integral from 0 to 20 of floor(x)^2 dx This is a classic step-function trap. Don’t try to “anti-differentiate” floor(x). Instead, split the interval into unit chunks and add rectangles. Once you see the pattern, it turns into a clean sum of squares. 👉 Hints • On [k, k 1), floor(x) = k. • Integral becomes sum_{k=0}^{19} k^2. • Use the formula for 1^2 2^2 … n^2. Would you spot the step-function strategy fast enough? ⏱️ 💭 Comment yo
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