3 ways: Find 1+2+3+ ... + n^2.

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

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Screen Recording 2024-05-12 at 10.20.08 PM

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

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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Pantun Melayu [Buah cempedak di luar pagar]

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2nd way: lim ((1+h)^3-1)/x? as h →0

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5 ways: integral ∫a^(px+q) dx

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2nd/2ways: count perm Show P(n,n)=P(n,n-1)

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Screen Recording 2024-05-12 at 8.34.35 PM

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1st/2ways: r-Permutations

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logic: Simplify the Boolean function F=AB+(AC)'+AB'C(AB+C)

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Screen Recording 2024-02-22 at 10.30.06 PM

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review: prob stat Population variance vs sample variance

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Screen Recording 2024-02-22 at 10.45.08 PM

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Screen Recording 2024-05-12 at 8.48.55 PM

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Columbia U: 10th/10 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub

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2nd way: trig 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫sin(x)cos(x)cos(4x)cos(8x)cos(16x)cos(32x)cos(64x) dx

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Careful: arc sin(sin(5π/4)) ≠ ...

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2nd/2ways: add math sum a + (a+d) + (a+2d) + ... + (a+(n-1)d) ?

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Screen Recording 2024-02-22 at 10.06.31 PM

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