trig integral ∫7x sin(x^2) sin(4x^2) dx

Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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

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lim x/e^x? as x→∞

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example Find 1+2+3+...+n via Pick's Theorem

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Black magic

Janica7474

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Screen Recording 2024-02-16 at 8.23.14 PM

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2024 #3 MIT Integration Bee Final Lightning Round

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prob stat: x̄=∑xk where k=1,2,3,...,n?

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2nd way: If y=(ax-b)/(a-bx), prove that 2y1y3=3(y2)^2

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Screen Recording 2024-02-21 at 10.01.27 PM

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Lamar U 2nd way: evaluate exp integral ∫e^(2x)/(1+e^(2x)) dx

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2nd way: trig Evaluate 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫ sin^3(x)/√cos(x) dx

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derivative: If x=cos(log(y)), show that (1-x^2)y2 - xy1 = y

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2024 MIT Integration Bee Final

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2nd/2ways: Taylor series of cos(x)

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Lamar U: #11 trig integral ∫csc^6(x/4) cot^4(x/4) dx

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prob stat: A population of N=5 scores has a mean µ= 12. What is ∑X for this sample?

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Who says you can only choose between love and opportunity? I'll let you go all in!

0011llyy

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prob stat: A die with 4 red faces & 2 green faces is rolled twice.

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