#16 MIT 2022 Integration Bee Qualifying Exam

Bijection of elements in tn & a pair of elements of (n+1)

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

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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review: When to use ... Sum of A.P n/2(a+l) vs n/2(2a+(n-1)d)

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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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prob stat: The following frequency table gives the values obtained

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Why the mean of AP is the median of AP? mean=median?

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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.

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

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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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logic: Simplify the Boolean function F=AB+(AC)'+AB'C(AB+C)

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2 ways: trig integral ∫1/(2+cos^2(x)) dx

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trig integral ∫tan^n(x) dx where n is EVEN via Reduction formula

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picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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

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#4 2017 MIT Integration Bee Qualifying Exam

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5 ways: integral ∫a^(px+q) dx

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UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]

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