Screen Recording 2024-02-22 at 10.18.05 PM

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

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2nd way: integral ∫ log √x(x^n) dx

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

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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Review: Linear form, Quadratic form & Bilinear form

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#9 2023 MIT Integration Bee Qualifying Exam

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2nd way: trig integral ∫1/(a+b sin(x)+c cos(x)) dx

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prob stat: Consider the experiment of tossing a fair coin twice & reading the up face on each toss.

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UC Davis#4 4 ways: integrate 7^(2x+3) dx

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A bag contains 5 red balls & 3 green balls. A ball is selected at random &

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UC Davis #8: integral cos(5x)/(3+sin(5x)) dx

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Review: Multiplying each obs. by a CONSTANT results in new variance =

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3 ways: exp integral ∫ln(e^x) + ln(e^(-x)) dx

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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1

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#17 2022 MIT Integration Bee Qualifying Exam

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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AP Calculus 2nd way: trig integral ∫dx/(4-3cos^2(x)+5sin^2(x)) dx

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exp integral ∫1/(e^(2x) - 25) dx

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2nd way: integral 1) ∫1/√(a - √b x^2)dx vs 2) ∫1/√(a - √b x^2) dx

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