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1st/2parts: Linear interpolation (2 given points)
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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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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(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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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
2nd way: integral ∫ log √x(x^n) dx
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trig integral ∫sin^5(x) dx
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count Show Σ k^2 = ΣΣmin(i,j) where i,j,k=1 to n
trig integral ∫1/(sin(ax) cos(ax)) dx
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Find the number of different 8 letter arrangements that can be made from the letters of the word ..
Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx
We lost original x's but still know mean x̄ & n. Now we collected m new observations.
picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n
Discrete rv X has the following prob. distribution
3rd/3 ways: How many chords can be drawn through 21 points on a circle?
#15 2022 MIT Integration Bee Qualifying Exam
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