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Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=
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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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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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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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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx
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2nd way: ∫2x/(x+5)^6 dx vs ∫2x (x+5)^6 dx
We lost original x's but still know mean x̄ & n. Now we collected m new observations.
#15 2022 MIT Integration Bee Qualifying Exam
picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n
#9 2023 MIT Integration Bee Qualifying Exam
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3rd/3 ways: How many chords can be drawn through 21 points on a circle?
prob stat: Compute Var(X) when X represents the outcome when we roll a fair die.
Find the number of different 8 letter arrangements that can be made from the letters of the word ..
2 ways: Find logarithm of 5 to the base 5 √5.
Simplify the following statements using only the connectives ∧, ∨ and ¬