2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?

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logic Idempotent law show x=xVx

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

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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

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integral ∫ x dx withOUT using Power rule.

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2nd way: ∫(x+3)/(x^2+6x)^2 dx vs ∫(x+3)(x^2+6x)^2 dx

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Find the expected value & the variance of a geometric r.v. X

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Screen Recording 2023-12-02 at 3.42.17 AM

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STPM Math T Sem.2 Exponential fun: Find the derivative (19)-(40)

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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2nd way: ∫1/(√(x-α)(x-β)) dx

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JHU: integral ∫t^3 e^(t^2) dt

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Conversion: Permutation - Combination vice versa

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2 ways: trig integral ∫1/(2+cos^2(x)) dx

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Screen Recording 2024-02-22 at 10.18.05 PM

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4 ways: trig integral ∫tan(x) dx

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Screen Recording 2023-12-06 at 3.07.30 AM

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UC Davis#2: 2nd way integral ∫(2x+3)/(x^2-9) dx [integration by partial fraction]

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Which of the following do NOT constitute a set & WHY?

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