CMU trig integral ∫sin^6(x) cos^3(x) dx

Calculus: If u=f(x+cy)+g(x-cy) then uxx / uyy ?

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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#2 2011 MIT Integration Bee Qualifying Exam

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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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2nd way: integral ∫1/x log mb(x) dx

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A cubical die, numbered 1 to 6 is weighted so that a six is twice as likely to occur as any other #.

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#2 2012 MIT Integration Bee Qualifying Exam

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2nd way: trig integral ∫sin(x)/(a-bcos(x)) dx

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prob stat: For events A & B it is known that P(A)=2/3, P(AuB)=3/4 & P(AnB)=5/12. Find P(B)

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prob stat: In how many ways can a hand of 4 cards be dealt from an ordinary pack of 52 playing cards

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

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2nd way: integral ∫1/(√(px-q) - √(px+r)) dx

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2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?

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2nd way: ∫2x/(x+5)^6 dx vs ∫2x (x+5)^6 dx

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Evaluate |x|/x for a)x gt 0 b) x lt 0

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Screen Recording 2024-05-19 at 11.13.23 PM

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#12 2012 MIT Integration Bee Qualifying Exam

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Screen Recording 2024-05-19 at 9.54.19 PM

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