prob stat: Find the expected value & std deviation in the number of '6's when 20 dice are rolled.

2024 MIT Integration Bee Final

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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

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

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lim x/e^x? as x→∞

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

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

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Let B be the mx1 col. matrix [1/m ... 1/m]'. If A =[a1 ... am] is any row matrix. What is AB?

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Lamar U: #11 trig integral ∫csc^6(x/4) cot^4(x/4) dx

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2nd way: trig integral ∫ 1/( √3 sin(x) + cos(x)) dx

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Screen Recording 2024-02-16 at 8.23.14 PM

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1998 AP Calculus BC: If dy/dx = (1-y^2), then d2y/dx2= ...

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2 ways: integral ∫ (4t+7) dt

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Gurjat CET-2007 2nd way log exp ∫e^(xln(2006) e^x dx

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1st/2 ways: MIT Integration Bee

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2nd way: trig sq rt Calculate integral ∫cos √x dx

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2nd way: integral ∫x^2 (x+1)^9 dx via withOUT u-sub

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2nd way: log sq rt integral ∫ln(x+1)/√(x+1) dx

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1st way: Calculate integral ∫x^2 (x+1)^9 dx

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#19 2011 MIT Integration Bee Qualifying Exam

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