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#12 2024 1st/2ways: MIT Integration Bee Qualifying Exam
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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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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NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)
prob stat: The following frequency table gives the values obtained
1st/2 ways: MIT Integration Bee
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2nd way: sq rt integral ∫(√x)/(x+1) dx
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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx
A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R
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Conversion: Permutation - Combination vice versa
UC Davis #14: integral ∫x √(4-x) dx
2nd way: ∫1/(√(1-x^2)(1+arc sin(x))^2) dx
2nd way: trig integral ∫(1-cos(x))(1+cos(x))/cos^2(x) dx
If P and Q are statements, then write the negation of P Q using only the connectives ∧ and ¬
Lamar U #12 trig integral sec^4(2t)/tan^9(2t) dt
#19 2010 MIT Integration Bee Qualifying Exam
#3 2023 MIT Integration Bee Qualifying Exam
00 Introduction