2 ways: trig integral ∫ sin^2(ax+b) dx

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

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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

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

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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2nd way: Find dy/dx a)x^y=y^x b)x^y+y^x=(x+y)^(x+y c) (cos(x))^y=(sin(y))^x

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What is π?

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prob stat: The p.d.f of a discrete r.v. Y is given by P(Y=y)=cy^2 for y=0,1,2,3,4.

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5 ways: integral ∫a^(px+q) dx

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

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prob stat: The discrete r.v. W has prob dist. as shown

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Screen Recording 2024-05-18 at 10.18.13 PM

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

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#9 2010 MIT Integration Bee Qualifying Exam

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prob stat: Events A & B are s.t P(A)=.3, P(B)=0.4, P(A n B)=0.1. Find a) P(AnB') b)P(A' n B')

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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx

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U Penn: Show that the following decomposition CANNOT hold ...

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Columbia U: 1st way integral ∫√(x^2-9)/x^4 dx

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Screen Recording 2023-12-07 at 2.04.49 AM

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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?

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