#4 2010 MIT Integration Bee Qualifying Exam

Compute the arithmetic mean for the following grouped data ...

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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count quick review: Permutation vs Combination

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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2 ways: sq root derivative 1/(√√(1/√x))

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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Swinburne U 2nd way: e^(-e^x) e^x dx

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Review: Linear form, Quadratic form & Bilinear form

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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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2 way: exp integral e^(ax+b)/1+e^(ax+b)) dx

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#4 2022 2nd/2 ways: MIT Integration Bee Qualifying Exam

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Screen Recording 2024-02-16 at 9.19.45 PM

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Columbia U: 10th/10 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub

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2nd way: trig integral ∫(sec(x) tan(x))/(sec^2(x)-sec(x)) dx

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#19 2011 MIT Integration Bee Qualifying Exam

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Screen Recording 2024-05-19 at 9.56.54 PM

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UC Davis: differentiate y=cos^2(x^3)

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2nd way: integral tan(x)/(1+tan(x)) dx

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