count Show Σ k^2 = ΣΣmin(i,j) where i,j,k=1 to n

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count quick review: Permutation vs Combination

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Pantun Melayu [Buah cempedak di luar pagar]

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Quickie: 6169^2 - 2331^2?

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2nd/3ways: exp Derivative x^x

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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2 ways: Σ 1? where k=m to n

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UC Davis #6: ∫ (2+tan(x))^2 dx

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alternate way: count sum 1+3+5+ ... +(2n-1)

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alternate way: count sum 1+2+3+ ... +n

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#6 2024 MIT Integration Bee Qualifying Exam

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MIT Integration Bee Qual. Exam #9: integral (2logx+1)e^(log(x))^2 dx

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3 ways: trig 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫sin(ax+b) dx

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2nd/2ways: Taylor series of cos(x)

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2 ways: trig integral ∫ sin^2(ax+b) dx

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Evaluate these 8 integrals of the form ∫(a-bx)^m dx

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UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]

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Alternate way: trig integral ∫sin(x) dx

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