MP-98 1st/2 ways Evaluate i) ∫e^(loge(x)) dx ii) ∫e^(-loge(x)) dx

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

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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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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2nd way: derivative ∫log (f(x))^g(x) (p(x))^r(x)

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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

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derivative If y=acos(log(x)) + bsin(log(x)), prove that x^2y2+xy1+y=0

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Given that X Geo(p), find P(X=k) if

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A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R

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A bag contains 20 identical red marbles, 20 identical green marbles, & 20 identical blue marbles.

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#17 2022 MIT Integration Bee Qualifying Exam

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

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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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1st/2 parts: Inverse 2x2 matrix

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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]

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Screen Recording 2023-12-07 at 2.09.05 AM

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trig integral sin(x+sin(x))-sin(x-sin(x)) dx

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#20 2022 MIT Integration Bee Qualifying Exam

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2nd way: integral ∫p^(nx) q^x dx

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