#15 2022 MIT Integration Bee Qualifying Exam

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Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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2nd way: integral ∫ log √x(x^n) dx

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

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Pantun Melayu [Buah cempedak di luar pagar]

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prpob stat A bag contains 5 black balls 6 red balls. Determine the number of ways in which ...

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Do you know ... in tagalog?

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

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U North Texas Integration Bee 2nd way: x^2/√(x-1) dx

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UT Austin: trig integral ∫18 tan^2(x) sec^2(x)/(2+tan^3(x))^2 dx

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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exp log derivative Know the differences ...

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logic Idempotent law show x=xVx

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logic Absorption law show x∧(x∨y)= y

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JEE Main integral ∫x^5 /√(1+x^3) dx

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logic implication distribute across disjunction: Show x→(y∨z) ≡ (x→y) ∨ (x→z)

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JEE Main integral x^2/(a+bx)^2 dx

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