UC Davis #14: integral ∫x √(4-x) dx

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

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inverse trig Derivative arc sin(x)

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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2nd way: integral ∫ log √x(x^n) dx

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Growing patterns #2

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Screen Recording 2024-05-12 at 10.20.08 PM

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Screen Recording 2024-05-12 at 8.48.55 PM

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Suppose f & g are positive functions. Obtain the product rule for (fg)' by differentiating ...

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What is π?

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2nd way: trig integral ∫1/(sin(x) cos^2(x)) dx

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2nd/4ways: trig derivative sin(x)

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3rd/3 parts: Growing patterns

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#Screen Recording 2024-05-13 at 10.52.38 PM

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3rd/3 ways: How many chords can be drawn through 21 points on a circle?

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3 ways: derivative e^y=x

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integral ∫(2x+3)/(4x^2+1) dx

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