1) integral ∫1/5 dx/(1+x) vs 2) integral ∫sec^(5x)/(1+ tan(5x)) dx

prob stat: One sample of n=4 scores has a mean of M=10, &

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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logic Idempotent law show x=xVx

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Review: Linear form, Quadratic form & Bilinear form

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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prob stat: 1st/2 parts. One sample has a mean of M=6 &

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2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub

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Lamar U #12 trig integral sec^4(2t)/tan^9(2t) dt

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Screen Recording 2024-05-05 at 11.28.23 PM

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2 ways: derivative √(x+1) √(x-1)

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Screen Recording 2023-12-06 at 3.07.30 AM

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2 ways: integral x√(x-5) dx

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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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UC Davis #1: 2 ways Find the length of the graph for y=3x+2 on the closed interval ...

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Find the expected value & the std deviation in the number of '6's when 20 dice are rolled.

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prob stat: A bag contains 5 red balls & 3 green balls. A ball is drawn at random &

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