2024 #3 MIT Integration Bee Final Lightning Round

034) L01 Atom and molecules NA

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2nd way: integral ∫ log √x(x^n) dx

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(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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2 ways: sq root derivative 1/(√√(1/√x))

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prob stat: One sample of n=4 scores has a mean of M=10, &

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Bachelor.Point.S05E39.720p.Bangla.AAC

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prob stat: 1st/2 parts. One sample has a mean of M=6 &

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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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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prob stat: A fair 6-sided dice, with sides numbered 1,1,2,2,3,55 is thrown.

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JHU: integral ∫t^3 e^(t^2) dt

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Solve the differential equation xcos^2(y) dx + tan(y) dy=0

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2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub

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Given events J & K:

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prob stat: A population of N=5 scores has a mean µ= 12. What is ∑X for this sample?

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Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5

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prob stat: A bag contains 5 red balls & 3 green balls. A ball is drawn at random &

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