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2024 #3 MIT Integration Bee Final Lightning Round
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2nd way: integral ∫ log √x(x^n) dx
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(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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pretend: to pretend
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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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#12 2012 MIT Integration Bee Qualifying Exam
Screen Recording 2024-02-16 at 9.14.39 PM
prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.
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#11 2014 MIT Integration Bee Qualifying Exam
2nd way: derivative (x^2+1)^sin(x)
2nd/2 ways: MIT Integration Bee Final
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Screen Recording 2024-02-16 at 8.23.14 PM
2nd/3ways: sum Show 1+2+3+...+n=n(1+n)/2
prob stat: A population of N=10 scores has a mean of 30.
Suppose your midterm test score is 83 & your final exam score is 95.
Show d/d(x/(x+1)) = d/dx(-1/(x+1)) ...