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#16 2011 MIT Integration Bee Qualifying Exam

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logic Show by truth table x∧(x→y)→y is Tautology
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logic Show by truth table x∧(x→y)→y is Tautology

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2nd way: integral ∫ log √x(x^n) 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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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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2nd/3ways: trig integral ∫sec(x) dx
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2nd/3ways: trig integral ∫sec(x) dx

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

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2nd way: ∫1/(√(x-α)(x-β)) dx
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2nd way: ∫1/(√(x-α)(x-β)) dx

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Calculus: Find nth derivative of log(ax+b)
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Calculus: Find nth derivative of log(ax+b)

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Suppose E & F are mutually exclusive events. Must E & F be complementary? Explain your answer.
3:48

Suppose E & F are mutually exclusive events. Must E & F be complementary? Explain your answer.

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2 ways: derivative x √√x
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2 ways: derivative x √√x

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Screen Recording 2024-02-22 at 10.09.39 PM
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Screen Recording 2024-02-22 at 10.09.39 PM

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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS
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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS

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AP Calculus 2nd way: integral ∫(ax+c)/(ax^2 + bx) dx
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AP Calculus 2nd way: integral ∫(ax+c)/(ax^2 + bx) dx

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

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2nd way: integral ∫x^(n-1) /(a-bx^n) dx
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2nd way: integral ∫x^(n-1) /(a-bx^n) dx

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Show integral ∫x √(ax+b) dx = 2(3ax-2b)√(ax+b)^3 /(15a^2)
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Show integral ∫x √(ax+b) dx = 2(3ax-2b)√(ax+b)^3 /(15a^2)

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2 ways: trig integral ∫tan^3(x) sec^2(x) dx
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2 ways: trig integral ∫tan^3(x) sec^2(x) dx

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#6 2024 MIT Integration Bee Qualifying Exam
1:24

#6 2024 MIT Integration Bee Qualifying Exam

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3 ways: If y=x/(1+x^2) find dy/dx.
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3 ways: If y=x/(1+x^2) find dy/dx.

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Screen Recording 2024-02-16 at 9.14.39 PM
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Screen Recording 2024-02-16 at 9.14.39 PM

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#4 2022 2nd/2 ways: MIT Integration Bee Qualifying Exam
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#4 2022 2nd/2 ways: MIT Integration Bee Qualifying Exam

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