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

prob stat: The following frequency table gives the values obtained

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count quick review: Permutation vs Combination

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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

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

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

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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Review: Linear form, Quadratic form & Bilinear form

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lim x/e^x? as x→∞

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Lamar U 2nd way: evaluate exp integral ∫e^(2x)/(1+e^(2x)) dx

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2 ways: trig integral ∫tan^3(x) sec^2(x) dx

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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.

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Roorkee 1976 RET 1991Hindustan: trig integral 1/(sin^2(x) cos^2(x)) dx

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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derivative If y=(a+bx)e^(-nx), prove that y2+2ny1+n^2y=0

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prob stat: Compute Var(X) when X represents the outcome when we roll a fair die.

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logic: De Morgan's Law

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Find the expected value & the variance of a geometric r.v. X

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Alternate way: derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2-xy1=a^2y

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Median [special weighted mean]

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