#14 2011 MIT Integration Bee Qualifying Exam

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

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

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

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

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logic Idempotent law show x=xVx

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logic Idempotent law show x=xVx

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Review: Linear form, Quadratic form & Bilinear form

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Review: Linear form, Quadratic form & Bilinear form

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

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

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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prob stat: The following frequency table gives the values obtained

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prob stat: The following frequency table gives the values obtained

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2nd way: trig integral ∫sin(x/a) dx

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2nd way: trig integral ∫sin(x/a) dx

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AP Calculus 2nd way trig integral ∫x^2 cos(x) dx

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AP Calculus 2nd way trig integral ∫x^2 cos(x) dx

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Show integral 1/(x^2(x^2+a^2)) dx = -1/(a^2x) - 1/a^3 arc tan(x/a)

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Show integral 1/(x^2(x^2+a^2)) dx = -1/(a^2x) - 1/a^3 arc tan(x/a)

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2nd way: Evaluate integral ∫x^2/√(19-x^2) dx

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2nd way: Evaluate integral ∫x^2/√(19-x^2) dx

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AP Calculus 2nd way: integral ∫ (3^(x+1)-7^(x-1))/21^x dx

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AP Calculus 2nd way: integral ∫ (3^(x+1)-7^(x-1))/21^x dx

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2nd way: trig integral ∫1/(1+sec(x)) dx

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2nd way: trig integral ∫1/(1+sec(x)) dx

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2024 MIT Integration Bee Final

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2024 MIT Integration Bee Final

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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS

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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS

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Variability or spread of a distribution. Whey we need it!

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Variability or spread of a distribution. Whey we need it!

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The sand in the desert stretches endlessly—why not use it to build houses? Let's hear the scientific

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The sand in the desert stretches endlessly—why not use it to build houses? Let's hear the scientific

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#14 2014 MIT Integration Bee Qualifying Exam

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#14 2014 MIT Integration Bee Qualifying Exam

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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