2 ways: integral ∫ 5x dx

Make.It.Right.S01E04- SUB ENG

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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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logic Idempotent law show x=xVx

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#12 2024 1st/2ways: MIT Integration Bee Qualifying Exam

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A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R

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prob stat: The following frequency table gives the values obtained

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Conversion: Permutation - Combination vice versa

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2nd way: sq rt integral ∫(√x)/(x+1) 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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4 ways: trig integral ∫tan(x) 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

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3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2

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alternate way: count sum 1+3+5+ ... +(2n-1)

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2nd way: ∫1/(√(1-x^2)(1+arc sin(x))^2) dx

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#3 2023 MIT Integration Bee Qualifying Exam

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4 ways: sum Find the sum of the values of 4+3i for i=1,2,...,100

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#19 2010 MIT Integration Bee Qualifying Exam

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alternate way: count sum 1+2+3+ ... +n

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