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logic: tautology (¬p→q)∧(¬p→¬q) →p
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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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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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2nd way: integral ∫ log √x(x^n) dx
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examples: 2x2 matrix which is its own inverse
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integral ∫logb(√x) dx
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There are 2 lines. One line has 3 points & the other line has 6 points.
alternate way: count sum 1+3+5+ ... +(2n-1)
STPM Math T Sem.2:
Show log b^n(x^m) = m/n logb(x)
exp integral ∫(1+e^x)/(1-e^x) dx
2 ways: Find the derivative y=x^n logb(x)
review: prob stat Population variance vs sample variance
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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"
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trig integral ∫sin(2x) cos(2x)/(9-cos^4(2x)) dx
Evaluate these 8 integrals of the form ∫(a-bx)^m dx
examples 2x2 matrix withOUT an inverse
trig integral ∫1/cos(ax+b) dx
3rd/3 ways: trig integral ∫ sin(ax+b) dx